From 22139c80dd5e2a530bb8efe9f7f47b18204c766d Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Wed, 2 Aug 2023 21:41:35 +0000 Subject: [PATCH] build based on b653323 --- stable | 2 +- v0.1 | 2 +- v0.1.8/ConservationLaws/index.html | 17 + v0.1.8/SpatialDiscretizations/index.html | 8 + v0.1.8/assets/documenter.js | 331 +++ v0.1.8/assets/favicon.ico | Bin 0 -> 4286 bytes v0.1.8/assets/favicon.png | Bin 0 -> 14746 bytes v0.1.8/assets/mesh.svg | 2652 +++++++++++++++++++++ v0.1.8/assets/meshmap.svg | 184 ++ v0.1.8/assets/ref_tri.svg | 141 ++ v0.1.8/assets/search.js | 267 +++ v0.1.8/assets/themes/documenter-dark.css | 7 + v0.1.8/assets/themes/documenter-light.css | 9 + v0.1.8/assets/themeswap.js | 66 + v0.1.8/assets/visualization.png | Bin 0 -> 3939639 bytes v0.1.8/assets/warner.js | 49 + v0.1.8/index.html | 2 + v0.1.8/search/index.html | 2 + v0.1.8/search_index.js | 3 + v0.1.8/siteinfo.js | 1 + versions.js | 2 +- 21 files changed, 3742 insertions(+), 3 deletions(-) create mode 100644 v0.1.8/ConservationLaws/index.html create mode 100644 v0.1.8/SpatialDiscretizations/index.html create mode 100644 v0.1.8/assets/documenter.js create mode 100644 v0.1.8/assets/favicon.ico create mode 100644 v0.1.8/assets/favicon.png create mode 100644 v0.1.8/assets/mesh.svg create mode 100644 v0.1.8/assets/meshmap.svg create mode 100644 v0.1.8/assets/ref_tri.svg create mode 100644 v0.1.8/assets/search.js create mode 100644 v0.1.8/assets/themes/documenter-dark.css create mode 100644 v0.1.8/assets/themes/documenter-light.css create mode 100644 v0.1.8/assets/themeswap.js create mode 100644 v0.1.8/assets/visualization.png create mode 100644 v0.1.8/assets/warner.js create mode 100644 v0.1.8/index.html create mode 100644 v0.1.8/search/index.html create mode 100644 v0.1.8/search_index.js create mode 100644 v0.1.8/siteinfo.js diff --git a/stable b/stable index 678367c22..3f0fd6bc9 120000 --- a/stable +++ b/stable @@ -1 +1 @@ -v0.1.7 \ No newline at end of file +v0.1.8 \ No newline at end of file diff --git a/v0.1 b/v0.1 index 678367c22..3f0fd6bc9 120000 --- a/v0.1 +++ b/v0.1 @@ -1 +1 @@ -v0.1.7 \ No newline at end of file +v0.1.8 \ No newline at end of file diff --git a/v0.1.8/ConservationLaws/index.html b/v0.1.8/ConservationLaws/index.html new file mode 100644 index 000000000..1b63f921a --- /dev/null +++ b/v0.1.8/ConservationLaws/index.html @@ -0,0 +1,17 @@ + +ConservationLaws · StableSpectralElements.jl

Module ConservationLaws

Overview

The equations to be solved are defined by subtypes of AbstractConservationLaw on which functions such as physical_flux and numerical_flux are dispatched. Objects of type AbstractConservationLaw contain two type parameters, d and PDEType, the former denoting the spatial dimension of the problem, which is inherited by all subtypes, and the latter being a subtype of AbstractPDEType denoting the particular type of PDE being solved, which is either FirstOrder or SecondOrder. Whereas first-order problems remove the dependence of the flux tensor on the solution gradient in order to obtain systems of the form

\[\partial_t \underline{U}(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \underline{\bm{F}}(\underline{U}(\bm{x},t)) = \underline{0},\]

second-order problems are treated by StableSpectralElements.jl as first-order systems of the form

\[\begin{aligned} +\underline{\bm{Q}}(\bm{x},t) - \bm{\nabla}_{\bm{x}} \underline{U}(\bm{x},t) &= \underline{0},\\ +\partial_t \underline{U}(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \underline{\bm{F}}(\underline{U}(\bm{x},t), \underline{\bm{Q}}(\bm{x},t)) &= \underline{0}. +\end{aligned}\]

Currently, the linear advection and advection-diffusion equations, the inviscid and viscous Burgers' equations, and the compressible Euler equations are supported by StableSpectralElements.jl, but any system of the above form can in principle be implemented, provided that appropriate physical and numerical fluxes are defined.

Equations

Listed below are partial differential equations supported by StableSpectralElements.jl.

StableSpectralElements.ConservationLaws.LinearAdvectionEquationType
LinearAdvectionEquation(a::NTuple{d,Float64}) where {d}

Define a linear advection equation of the form

\[\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big( \bm{a} U(\bm{x},t) \big) = 0,\]

with a constant advection velocity $\bm{a} \in \R^d$. A specialized constructor LinearAdvectionEquation(a::Float64) is provided for the one-dimensional case.

source
StableSpectralElements.ConservationLaws.LinearAdvectionDiffusionEquationType
LinearAdvectionDiffusionEquation(a::NTuple{d,Float64}, b::Float64) where {d}

Define a linear advection-diffusion equation of the form

\[\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big( \bm{a} U(\bm{x},t) - b \bm{\nabla} U(\bm{x},t)\big) = 0,\]

with a constant advection velocity $\bm{a} \in \R^d$ and diffusion coefficient $b \in \R^+$. A specialized constructor LinearAdvectionDiffusionEquation(a::Float64, b::Float64) is provided for the one-dimensional case.

source
StableSpectralElements.ConservationLaws.InviscidBurgersEquationType
InviscidBurgersEquation(a::NTuple{d,Float64}) where {d}

Define an inviscid Burgers' equation of the form

\[\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 \big) = 0,\]

where $\bm{a} \in \R^d$. A specialized constructor InviscidBurgersEquation() is provided for the one-dimensional case with a = (1.0,).

source
StableSpectralElements.ConservationLaws.ViscousBurgersEquationType
ViscousBurgersEquation(a::NTuple{d,Float64}, b::Float64) where {d}

Define a viscous Burgers' equation of the form

\[\partial_t U(\bm{x},t) + \bm{\nabla} \cdot \big(\tfrac{1}{2}\bm{a} U(\bm{x},t)^2 - b \bm{\nabla} U(\bm{x},t)\big) = 0,\]

where $\bm{a} \in \R^d$ and $b \in \R^+$. A specialized constructor ViscousBurgersEquation(b::Float64) is provided for the one-dimensional case with a = (1.0,).

source
StableSpectralElements.ConservationLaws.EulerEquationsType
EulerEquations{d}(γ::Float64) where {d}

Define an Euler system governing compressible, adiabatic fluid flow, taking the form

\[\frac{\partial}{\partial t}\left[\begin{array}{c} +\rho(\bm{x}, t) \\ +\rho(\bm{x}, t) V_1(\bm{x}, t) \\ +\vdots \\ +\rho(\bm{x}, t) V_d(\bm{x}, t) \\ +E(\bm{x}, t) +\end{array}\right]+\sum_{m=1}^d \frac{\partial}{\partial x_m}\left[\begin{array}{c} +\rho(\bm{x}, t) V_m(\bm{x}, t) \\ +\rho(\bm{x}, t) V_1(\bm{x}, t) V_m(\bm{x}, t)+P(\bm{x}, t) \delta_{1 m} \\ +\vdots \\ +\rho(\bm{x}, t) V_d(\bm{x}, t) V_m(\bm{x}, t)+P(\bm{x}, t) \delta_{d m} \\ +V_m(\bm{x}, t)(E(\bm{x}, t)+P(\bm{x}, t)) +\end{array}\right]=\underline{0},\]

where $\rho(\bm{x},t) \in \mathbb{R}$ is the fluid density, $\bm{V}(\bm{x},t) \in \mathbb{R}^d$ is the flow velocity, $E(\bm{x},t) \in \mathbb{R}$ is the total energy per unit volume, and the pressure is given for an ideal gas with constant specific heat as

\[P(\bm{x},t) = (\gamma - 1)\Big(E(\bm{x},t) - \frac{1}{2}\rho(\bm{x},t) \lVert \bm{V}(\bm{x},t)\rVert^2\Big).\]

The specific heat ratio is specified as a parameter γ::Float64, which must be greater than unity.

source
diff --git a/v0.1.8/SpatialDiscretizations/index.html b/v0.1.8/SpatialDiscretizations/index.html new file mode 100644 index 000000000..585c1e425 --- /dev/null +++ b/v0.1.8/SpatialDiscretizations/index.html @@ -0,0 +1,8 @@ + +SpatialDiscretizations · StableSpectralElements.jl

Module SpatialDiscretizations

Overview

Discretizations in StableSpectralElements.jl are constructed by first building a local approximation on a canonical reference element, denoted generically as $\hat{\Omega} \subset \mathbb{R}^d$, and using a bijective transformation $\bm{X}^{(\kappa)} : \hat{\Omega} \rightarrow \Omega^{(\kappa)}$ to construct the approximation on each physical element of the mesh $\mathcal{T}^h = \{ \Omega^{(\kappa)}\}_{\kappa \in \{1:N_e\}}$ in terms of the associated operators on the reference element. An example of such a mapping is shown below.

Mesh mapping

In order to define the different geometric reference elements, existing subtypes of AbstractElemShape from StartUpDG.jl (e.g. Line, Quad, Hex, Tri, and Tet) are used and re-exported by StableSpectralElements.jl. For example, we have

\[\begin{aligned} +\hat{\Omega}_{\mathrm{line}} &= [-1,1],\\ +\hat{\Omega}_{\mathrm{quad}} &= [-1,1]^2,\\ +\hat{\Omega}_{\mathrm{hex}} & = [-1,1]^3, \\ +\hat{\Omega}_{\mathrm{tri}} &= \big\{ \bm{\xi} \in [-1,1]^2 : \xi_1 + \xi_2 \leq 0 \big\},\\ +\hat{\Omega}_{\mathrm{tet}} &= \big\{ \bm{\xi} \in [-1,1]^3 : \xi_1 + \xi_2 + \xi_3 \leq -1 \big\}. +\end{aligned}\]

These element types are used in the constructor for StableSpectralElements.jl's ReferenceApproximation type, along with a subtype of AbstractApproximationType specifying the nature of the local approximation (and, optionally, the associated volume and facet quadrature rules).

All the information used to define the spatial discretization on the physical domain $\Omega$ is contained within a SpatialDiscretization structure, which is constructed using a ReferenceApproximation and a MeshData from StartUpDG.jl, which are stored as the fields reference_approximation and mesh. When the constructor for a SpatialDiscretization is called, the grid metrics are computed and stored in a GeometricFactors structure, with the corresponding field being geometric_factors.

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/dev/null +++ b/v0.1.8/assets/search.js @@ -0,0 +1,267 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.9/lunr.min', + 'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.21/lodash.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.6.0/jquery.min', + } +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'lunr', 'lodash'], function($, lunr, _) { + +$(document).ready(function() { + // parseUri 1.2.2 + // (c) Steven Levithan + // MIT License + function parseUri (str) { + var o = parseUri.options, + m = o.parser[o.strictMode ? "strict" : "loose"].exec(str), + uri = {}, + i = 14; + + while (i--) uri[o.key[i]] = m[i] || ""; + + uri[o.q.name] = {}; + uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) { + if ($1) uri[o.q.name][$1] = $2; + }); + + return uri; + }; + parseUri.options = { + strictMode: false, + key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"], + q: { + name: "queryKey", + parser: /(?:^|&)([^&=]*)=?([^&]*)/g + }, + parser: { + strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/, + loose: /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/ + } + }; + + $("#search-form").submit(function(e) { + e.preventDefault() + }) + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + lunr.stopWordFilter = lunr.generateStopWordFilter([ + 'a', + 'able', + 'about', + 'across', + 'after', + 'almost', + 'also', + 'am', + 'among', + 'an', + 'and', + 'are', + 'as', + 'at', + 'be', + 'because', + 'been', + 'but', + 'by', + 'can', + 'cannot', + 'could', + 'dear', + 'did', + 'does', + 'either', + 'ever', + 'every', + 'from', + 'got', + 'had', + 'has', + 'have', + 'he', + 'her', + 'hers', + 'him', + 'his', + 'how', + 'however', + 'i', + 'if', + 'into', + 'it', + 'its', + 'just', + 'least', + 'like', + 'likely', + 'may', + 'me', + 'might', + 'most', + 'must', + 'my', + 'neither', + 'no', + 'nor', + 'not', + 'of', + 'off', + 'often', + 'on', + 'or', + 'other', + 'our', + 'own', + 'rather', + 'said', + 'say', + 'says', + 'she', + 'should', + 'since', + 'so', + 'some', + 'than', + 'that', + 'the', + 'their', + 'them', + 'then', + 'there', + 'these', + 'they', + 'this', + 'tis', + 'to', + 'too', + 'twas', + 'us', + 'wants', + 'was', + 'we', + 'were', + 'what', + 'when', + 'who', + 'whom', + 'why', + 'will', + 'would', + 'yet', + 'you', + 'your' + ]) + + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!" + // would not find anything if searching for "add!", only for the entire qualification + lunr.tokenizer.separator = /[\s\-\.]+/ + + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + lunr.trimmer = function (token) { + return token.update(function (s) { + return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '') + }) + } + + lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter') + lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer') + + var index = lunr(function () { + this.ref('location') + this.field('title',{boost: 100}) + this.field('text') + documenterSearchIndex['docs'].forEach(function(e) { + this.add(e) + }, this) + }) + var store = {} + + documenterSearchIndex['docs'].forEach(function(e) { + store[e.location] = {title: e.title, category: e.category, page: e.page} + }) + + $(function(){ + searchresults = $('#documenter-search-results'); + searchinfo = $('#documenter-search-info'); + searchbox = $('#documenter-search-query'); + searchform = $('.docs-search'); + sidebar = $('.docs-sidebar'); + function update_search(querystring) { + tokens = lunr.tokenizer(querystring) + results = index.query(function (q) { + tokens.forEach(function (t) { + q.term(t.toString(), { + fields: ["title"], + boost: 100, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["title"], + boost: 10, + usePipeline: true, + editDistance: 2, + wildcard: lunr.Query.wildcard.NONE + }) + q.term(t.toString(), { + fields: ["text"], + boost: 1, + usePipeline: true, + editDistance: 0, + wildcard: lunr.Query.wildcard.NONE + }) + }) + }) + searchinfo.text("Number of results: " + results.length) + searchresults.empty() + results.forEach(function(result) { + data = store[result.ref] + link = $(''+data.title+'') + link.attr('href', documenterBaseURL+'/'+result.ref) + if (data.category != "page"){ + cat = $('('+data.category+', '+data.page+')') + } else { + cat = $('('+data.category+')') + } + li = $('
  • ').append(link).append(" ").append(cat) + searchresults.append(li) + }) + } + + function update_search_box() { + querystring = searchbox.val() + update_search(querystring) + } + + searchbox.keyup(_.debounce(update_search_box, 250)) + searchbox.change(update_search_box) + + // Disable enter-key form submission for the searchbox on the search page + // and just re-run search rather than refresh the whole page. + searchform.keypress( + function(event){ + if (event.which == '13') { + if (sidebar.hasClass('visible')) { + sidebar.removeClass('visible'); + } + update_search_box(); + event.preventDefault(); + } + } + ); + + search_query_uri = parseUri(window.location).queryKey["q"] + if(search_query_uri !== undefined) { + search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20')) + searchbox.val(search_query) + } + update_search_box(); + }) +}) + +}) diff --git a/v0.1.8/assets/themes/documenter-dark.css b/v0.1.8/assets/themes/documenter-dark.css new file mode 100644 index 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ecf0f1 #ecf0f1 !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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.button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #282f2f #282f2f !important}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--documenter-dark .content 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form.docs-search>input.button{border-radius:290486px;padding-left:1em;padding-right:1em}html.theme--documenter-dark .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--documenter-dark .buttons .button{margin-bottom:0.5rem}html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:0.5rem}html.theme--documenter-dark .buttons:last-child{margin-bottom:-0.5rem}html.theme--documenter-dark .buttons:not(:last-child){margin-bottom:1rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){border-radius:3px;font-size:.85em}html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--documenter-dark .buttons.has-addons 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a.navbar-item,html.theme--documenter-dark .navbar-link{cursor:pointer}html.theme--documenter-dark a.navbar-item:focus,html.theme--documenter-dark a.navbar-item:focus-within,html.theme--documenter-dark a.navbar-item:hover,html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link:focus,html.theme--documenter-dark .navbar-link:focus-within,html.theme--documenter-dark .navbar-link:hover,html.theme--documenter-dark .navbar-link.is-active{background-color:rgba(0,0,0,0);color:#1abc9c}html.theme--documenter-dark .navbar-item{display:block;flex-grow:0;flex-shrink:0}html.theme--documenter-dark .navbar-item img{max-height:1.75rem}html.theme--documenter-dark .navbar-item.has-dropdown{padding:0}html.theme--documenter-dark .navbar-item.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .navbar-item.is-tab{border-bottom:1px solid transparent;min-height:4rem;padding-bottom:calc(0.5rem - 1px)}html.theme--documenter-dark 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1055px){html.theme--documenter-dark .navbar>.container{display:block}html.theme--documenter-dark .navbar-brand .navbar-item,html.theme--documenter-dark .navbar-tabs .navbar-item{align-items:center;display:flex}html.theme--documenter-dark .navbar-link::after{display:none}html.theme--documenter-dark .navbar-menu{background-color:#375a7f;box-shadow:0 8px 16px rgba(10,10,10,0.1);padding:0.5rem 0}html.theme--documenter-dark .navbar-menu.is-active{display:block}html.theme--documenter-dark .navbar.is-fixed-bottom-touch,html.theme--documenter-dark .navbar.is-fixed-top-touch{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-touch{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-touch{top:0}html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu,html.theme--documenter-dark .navbar.is-fixed-top-touch 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a.navbar-item:hover{background-color:rgba(0,0,0,0);color:#dbdee0}html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active{background-color:rgba(0,0,0,0);color:#1abc9c}.navbar.is-spaced html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop{bottom:0}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow{box-shadow:0 -2px 3px rgba(10,10,10,0.1)}html.theme--documenter-dark .navbar.is-fixed-top-desktop{top:0}html.theme--documenter-dark html.has-navbar-fixed-top-desktop,html.theme--documenter-dark body.has-navbar-fixed-top-desktop{padding-top:4rem}html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop{padding-bottom:4rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-top,html.theme--documenter-dark body.has-spaced-navbar-fixed-top{padding-top:6rem}html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom{padding-bottom:6rem}html.theme--documenter-dark a.navbar-item.is-active,html.theme--documenter-dark .navbar-link.is-active{color:#1abc9c}html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:15px;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.85em}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-previous,html.theme--documenter-dark .pagination.is-rounded .pagination-next,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-next{padding-left:1em;padding-right:1em;border-radius:290486px}html.theme--documenter-dark .pagination.is-rounded .pagination-link,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination .pagination-link{border-radius:290486px}html.theme--documenter-dark .pagination,html.theme--documenter-dark .pagination-list{align-items:center;display:flex;justify-content:center;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis{font-size:1em;justify-content:center;margin:.25rem;padding-left:.5em;padding-right:.5em;text-align:center}html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link{border-color:#5e6d6f;color:#1abc9c;min-width:2.25em}html.theme--documenter-dark .pagination-previous:hover,html.theme--documenter-dark .pagination-next:hover,html.theme--documenter-dark .pagination-link:hover{border-color:#8c9b9d;color:#1dd2af}html.theme--documenter-dark .pagination-previous:focus,html.theme--documenter-dark .pagination-next:focus,html.theme--documenter-dark .pagination-link:focus{border-color:#8c9b9d}html.theme--documenter-dark .pagination-previous:active,html.theme--documenter-dark .pagination-next:active,html.theme--documenter-dark .pagination-link:active{box-shadow:inset 0 1px 2px rgba(10,10,10,0.2)}html.theme--documenter-dark .pagination-previous[disabled],html.theme--documenter-dark 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ul.is-center{flex:none;justify-content:center;padding-left:0.75em;padding-right:0.75em}html.theme--documenter-dark .tabs ul.is-right{justify-content:flex-end;padding-left:0.75em}html.theme--documenter-dark .tabs .icon:first-child{margin-right:0.5em}html.theme--documenter-dark .tabs .icon:last-child{margin-left:0.5em}html.theme--documenter-dark .tabs.is-centered ul{justify-content:center}html.theme--documenter-dark .tabs.is-right ul{justify-content:flex-end}html.theme--documenter-dark .tabs.is-boxed a{border:1px solid transparent;border-radius:.4em .4em 0 0}html.theme--documenter-dark .tabs.is-boxed a:hover{background-color:#282f2f;border-bottom-color:#5e6d6f}html.theme--documenter-dark .tabs.is-boxed li.is-active a{background-color:#fff;border-color:#5e6d6f;border-bottom-color:rgba(0,0,0,0) !important}html.theme--documenter-dark .tabs.is-fullwidth li{flex-grow:1;flex-shrink:0}html.theme--documenter-dark .tabs.is-toggle 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Gets put into the tag.. +function set_theme_from_local_storage() { + // Intialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if(window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the browser supports user color preference + var darkPreference = false; + // Check if the users preference is for dark color scheme + if(window.matchMedia('(prefers-color-scheme: dark)').matches === true) { + darkPreference = true; + } + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; var disabled = []; var darkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if(themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + var isprimary = (ss.ownerNode.getAttribute("data-theme-primary") !== null); + // Check if the theme is primary dark theme + var isDarkTheme = (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null); + // If ss is for dark theme then set the value of darkTheme to the name of the theme + if(isDarkTheme) darkTheme = themename; + // If we find a matching theme (and it's not the default), we'll set active to non-null + if(themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if(themename !== theme) disabled.push(ss); + } + if(active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class 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stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +}; + +if (document.readyState === 'loading') { + document.addEventListener('DOMContentLoaded', maybeAddWarning); +} else { + maybeAddWarning(); +}; diff --git a/v0.1.8/index.html b/v0.1.8/index.html new file mode 100644 index 000000000..e233d6c02 --- /dev/null +++ b/v0.1.8/index.html @@ -0,0 +1,2 @@ + +Home · StableSpectralElements.jl

    StableSpectralElements.jl

    StableSpectralElements.jl, formerly known as CLOUD.jl (Conservation Laws on Unstructured Domains), is a Julia framework for the numerical solution of partial differential equations of the form

    \[\partial_t \underline{U}(\bm{x},t) + \bm{\nabla}_{\bm{x}} \cdot \underline{\bm{F}}(\underline{U}(\bm{x},t), \bm{\nabla}_{\bm{x}}\underline{U}(\bm{x},t)) = \underline{0},\]

    for $t \in (0,T)$ with $T \in \mathbb{R}^+ $ and $\bm{x} \in \Omega \subset \mathbb{R}^d$, subject to appropriate initial and boundary conditions, where $\underline{U}(\bm{x},t)$ is the vector of solution variables and $\underline{\bm{F}}(\underline{U}(\bm{x},t),\bm{\nabla}_{\bm{x}}\underline{U}(\bm{x},t))$ is the flux tensor containing advective and/or diffusive contributions. These equations are spatially discretized on curvilinear unstructured grids using energy-stable and entropy-stable discontinuous spectral element methods in order to generate ODEProblem objects suitable for time integration using OrdinaryDiffEq.jl within the SciML ecosystem. StableSpectralElements.jl also includes postprocessing tools employing WriteVTK.jl for generating .vtu files, allowing for visualization of high-order numerical solutions on unstructured grids using ParaView or other software. Shared-memory parallelization is supported through multithreading.

    The functionality provided by StartUpDG.jl for the handling of mesh data structures, polynomial basis functions, and quadrature nodes is employed throughout this package. Moreover, StableSpectralElements.jl implements dispatched strategies for semi-discrete operator evaluation using LinearMaps.jl, allowing for the efficient matrix-free application of tensor-product operators.

    Discretizations satisfying the summation-by-parts property employing nodal as well as modal bases are implemented, with the latter allowing for efficient and low-storage inversion of the dense elemental mass matrices arising from curvilinear meshes through the use of weight-adjusted approximations.

    Installation

    StableSpectralElements.jl is a registered Julia package (compatible with Julia versions 1.8 and higher) and can be installed by entering the following commands within the REPL:

    using Pkg; Pkg.add("StableSpectralElements")

    Examples

    We recommend that users refer to the following Jupyter notebooks (included in the examples directory) for examples of how to use StableSpectralElements.jl:

    License

    This software is released under the GPLv3 license.

    diff --git a/v0.1.8/search/index.html b/v0.1.8/search/index.html new file mode 100644 index 000000000..231bfbf9b --- /dev/null +++ b/v0.1.8/search/index.html @@ -0,0 +1,2 @@ + +Search · StableSpectralElements.jl

    Loading search...

      diff --git a/v0.1.8/search_index.js b/v0.1.8/search_index.js new file mode 100644 index 000000000..398a54c1c --- /dev/null +++ b/v0.1.8/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"SpatialDiscretizations/#Module-SpatialDiscretizations","page":"SpatialDiscretizations","title":"Module SpatialDiscretizations","text":"","category":"section"},{"location":"SpatialDiscretizations/#Overview","page":"SpatialDiscretizations","title":"Overview","text":"","category":"section"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"Discretizations in StableSpectralElements.jl are constructed by first building a local approximation on a canonical reference element, denoted generically as hatOmega subset mathbbR^d, and using a bijective transformation bmX^(kappa) hatOmega rightarrow Omega^(kappa) to construct the approximation on each physical element of the mesh mathcalT^h = Omega^(kappa)_kappa in 1N_e in terms of the associated operators on the reference element. An example of such a mapping is shown below.","category":"page"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"(Image: Mesh mapping)","category":"page"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"In order to define the different geometric reference elements, existing subtypes of AbstractElemShape from StartUpDG.jl (e.g. Line, Quad, Hex, Tri, and Tet) are used and re-exported by StableSpectralElements.jl. For example, we have ","category":"page"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"beginaligned\nhatOmega_mathrmline = -11\nhatOmega_mathrmquad = -11^2\nhatOmega_mathrmhex = -11^3 \nhatOmega_mathrmtri = big bmxi in -11^2 xi_1 + xi_2 leq 0 big\nhatOmega_mathrmtet = big bmxi in -11^3 xi_1 + xi_2 + xi_3 leq -1 big\nendaligned","category":"page"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"These element types are used in the constructor for StableSpectralElements.jl's ReferenceApproximation type, along with a subtype of AbstractApproximationType specifying the nature of the local approximation (and, optionally, the associated volume and facet quadrature rules).","category":"page"},{"location":"SpatialDiscretizations/","page":"SpatialDiscretizations","title":"SpatialDiscretizations","text":"All the information used to define the spatial discretization on the physical domain Omega is contained within a SpatialDiscretization structure, which is constructed using a ReferenceApproximation and a MeshData from StartUpDG.jl, which are stored as the fields reference_approximation and mesh. When the constructor for a SpatialDiscretization is called, the grid metrics are computed and stored in a GeometricFactors structure, with the corresponding field being geometric_factors. ","category":"page"},{"location":"ConservationLaws/#Module-ConservationLaws","page":"ConservationLaws","title":"Module ConservationLaws","text":"","category":"section"},{"location":"ConservationLaws/#Overview","page":"ConservationLaws","title":"Overview","text":"","category":"section"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"The equations to be solved are defined by subtypes of AbstractConservationLaw on which functions such as physical_flux and numerical_flux are dispatched. Objects of type AbstractConservationLaw contain two type parameters, d and PDEType, the former denoting the spatial dimension of the problem, which is inherited by all subtypes, and the latter being a subtype of AbstractPDEType denoting the particular type of PDE being solved, which is either FirstOrder or SecondOrder. Whereas first-order problems remove the dependence of the flux tensor on the solution gradient in order to obtain systems of the form","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"partial_t underlineU(bmxt) + bmnabla_bmx cdot underlinebmF(underlineU(bmxt)) = underline0","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"second-order problems are treated by StableSpectralElements.jl as first-order systems of the form ","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"beginaligned\nunderlinebmQ(bmxt) - bmnabla_bmx underlineU(bmxt) = underline0\npartial_t underlineU(bmxt) + bmnabla_bmx cdot underlinebmF(underlineU(bmxt) underlinebmQ(bmxt)) = underline0\nendaligned","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"Currently, the linear advection and advection-diffusion equations, the inviscid and viscous Burgers' equations, and the compressible Euler equations are supported by StableSpectralElements.jl, but any system of the above form can in principle be implemented, provided that appropriate physical and numerical fluxes are defined.","category":"page"},{"location":"ConservationLaws/#Equations","page":"ConservationLaws","title":"Equations","text":"","category":"section"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"Listed below are partial differential equations supported by StableSpectralElements.jl.","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":"CurrentModule = ConservationLaws","category":"page"},{"location":"ConservationLaws/","page":"ConservationLaws","title":"ConservationLaws","text":" LinearAdvectionEquation\n LinearAdvectionDiffusionEquation\n InviscidBurgersEquation\n ViscousBurgersEquation\n EulerEquations","category":"page"},{"location":"ConservationLaws/#StableSpectralElements.ConservationLaws.LinearAdvectionEquation","page":"ConservationLaws","title":"StableSpectralElements.ConservationLaws.LinearAdvectionEquation","text":"LinearAdvectionEquation(a::NTuple{d,Float64}) where {d}\n\nDefine a linear advection equation of the form\n\npartial_t U(bmxt) + bmnabla cdot big( bma U(bmxt) big) = 0\n\nwith a constant advection velocity bma in R^d. A specialized constructor LinearAdvectionEquation(a::Float64) is provided for the one-dimensional case.\n\n\n\n\n\n","category":"type"},{"location":"ConservationLaws/#StableSpectralElements.ConservationLaws.LinearAdvectionDiffusionEquation","page":"ConservationLaws","title":"StableSpectralElements.ConservationLaws.LinearAdvectionDiffusionEquation","text":"LinearAdvectionDiffusionEquation(a::NTuple{d,Float64}, b::Float64) where {d}\n\nDefine a linear advection-diffusion equation of the form\n\npartial_t U(bmxt) + bmnabla cdot big( bma U(bmxt) - b bmnabla U(bmxt)big) = 0\n\nwith a constant advection velocity bma in R^d and diffusion coefficient b in R^+. A specialized constructor LinearAdvectionDiffusionEquation(a::Float64, b::Float64) is provided for the one-dimensional case.\n\n\n\n\n\n","category":"type"},{"location":"ConservationLaws/#StableSpectralElements.ConservationLaws.InviscidBurgersEquation","page":"ConservationLaws","title":"StableSpectralElements.ConservationLaws.InviscidBurgersEquation","text":"InviscidBurgersEquation(a::NTuple{d,Float64}) where {d}\n\nDefine an inviscid Burgers' equation of the form\n\npartial_t U(bmxt) + bmnabla cdot big(tfrac12bma U(bmxt)^2 big) = 0\n\nwhere bma in R^d. A specialized constructor InviscidBurgersEquation() is provided for the one-dimensional case with a = (1.0,).\n\n\n\n\n\n","category":"type"},{"location":"ConservationLaws/#StableSpectralElements.ConservationLaws.ViscousBurgersEquation","page":"ConservationLaws","title":"StableSpectralElements.ConservationLaws.ViscousBurgersEquation","text":"ViscousBurgersEquation(a::NTuple{d,Float64}, b::Float64) where {d}\n\nDefine a viscous Burgers' equation of the form\n\npartial_t U(bmxt) + bmnabla cdot big(tfrac12bma U(bmxt)^2 - b bmnabla U(bmxt)big) = 0\n\nwhere bma in R^d and b in R^+. A specialized constructor ViscousBurgersEquation(b::Float64) is provided for the one-dimensional case with a = (1.0,).\n\n\n\n\n\n","category":"type"},{"location":"ConservationLaws/#StableSpectralElements.ConservationLaws.EulerEquations","page":"ConservationLaws","title":"StableSpectralElements.ConservationLaws.EulerEquations","text":"EulerEquations{d}(γ::Float64) where {d}\n\nDefine an Euler system governing compressible, adiabatic fluid flow, taking the form\n\nfracpartialpartial tleftbeginarrayc\nrho(bmx t) \nrho(bmx t) V_1(bmx t) \nvdots \nrho(bmx t) V_d(bmx t) \nE(bmx t)\nendarrayright+sum_m=1^d fracpartialpartial x_mleftbeginarrayc\nrho(bmx t) V_m(bmx t) \nrho(bmx t) V_1(bmx t) V_m(bmx t)+P(bmx t) delta_1 m \nvdots \nrho(bmx t) V_d(bmx t) V_m(bmx t)+P(bmx t) delta_d m \nV_m(bmx t)(E(bmx t)+P(bmx t))\nendarrayright=underline0\n\nwhere rho(bmxt) in mathbbR is the fluid density, bmV(bmxt) in mathbbR^d is the flow velocity, E(bmxt) in mathbbR is the total energy per unit volume, and the pressure is given for an ideal gas with constant specific heat as\n\nP(bmxt) = (gamma - 1)Big(E(bmxt) - frac12rho(bmxt) lVert bmV(bmxt)rVert^2Big)\n\nThe specific heat ratio is specified as a parameter γ::Float64, which must be greater than unity.\n\n\n\n\n\n","category":"type"},{"location":"#StableSpectralElements.jl","page":"Home","title":"StableSpectralElements.jl","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"StableSpectralElements.jl, formerly known as CLOUD.jl (Conservation Laws on Unstructured Domains), is a Julia framework for the numerical solution of partial differential equations of the form","category":"page"},{"location":"","page":"Home","title":"Home","text":"partial_t underlineU(bmxt) + bmnabla_bmx cdot underlinebmF(underlineU(bmxt) bmnabla_bmxunderlineU(bmxt)) = underline0","category":"page"},{"location":"","page":"Home","title":"Home","text":"for t in (0T) with T in mathbbR^+ and bmx in Omega subset mathbbR^d, subject to appropriate initial and boundary conditions, where underlineU(bmxt) is the vector of solution variables and underlinebmF(underlineU(bmxt)bmnabla_bmxunderlineU(bmxt)) is the flux tensor containing advective and/or diffusive contributions. These equations are spatially discretized on curvilinear unstructured grids using energy-stable and entropy-stable discontinuous spectral element methods in order to generate ODEProblem objects suitable for time integration using OrdinaryDiffEq.jl within the SciML ecosystem. StableSpectralElements.jl also includes postprocessing tools employing WriteVTK.jl for generating .vtu files, allowing for visualization of high-order numerical solutions on unstructured grids using ParaView or other software. Shared-memory parallelization is supported through multithreading.","category":"page"},{"location":"","page":"Home","title":"Home","text":"The functionality provided by StartUpDG.jl for the handling of mesh data structures, polynomial basis functions, and quadrature nodes is employed throughout this package. Moreover, StableSpectralElements.jl implements dispatched strategies for semi-discrete operator evaluation using LinearMaps.jl, allowing for the efficient matrix-free application of tensor-product operators.","category":"page"},{"location":"","page":"Home","title":"Home","text":"Discretizations satisfying the summation-by-parts property employing nodal as well as modal bases are implemented, with the latter allowing for efficient and low-storage inversion of the dense elemental mass matrices arising from curvilinear meshes through the use of weight-adjusted approximations. ","category":"page"},{"location":"#Installation","page":"Home","title":"Installation","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"StableSpectralElements.jl is a registered Julia package (compatible with Julia versions 1.8 and higher) and can be installed by entering the following commands within the REPL:","category":"page"},{"location":"","page":"Home","title":"Home","text":"using Pkg; Pkg.add(\"StableSpectralElements\")","category":"page"},{"location":"#Examples","page":"Home","title":"Examples","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"We recommend that users refer to the following Jupyter notebooks (included in the examples directory) for examples of how to use StableSpectralElements.jl:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Linear advection-diffusion equation in 1D\nInviscid Burgers' equation in 1D with energy-conservative scheme\nEuler equations in 1D with entropy-conservative Gauss collocation methods\nLinear advection equation in 2D\nIsentropic Euler vortex in 2D with entropy-stable modal scheme on triangles\nLinear advection equation in 3D","category":"page"},{"location":"#License","page":"Home","title":"License","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"This software is released under the GPLv3 license.","category":"page"}] +} diff --git a/v0.1.8/siteinfo.js b/v0.1.8/siteinfo.js new file mode 100644 index 000000000..547a8675f --- /dev/null +++ b/v0.1.8/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.8"; diff --git a/versions.js b/versions.js index d903b674c..3fcdf5956 100644 --- a/versions.js +++ b/versions.js @@ -3,5 +3,5 @@ var DOC_VERSIONS = [ "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "v0.1.7"; +var DOCUMENTER_NEWEST = "v0.1.8"; var DOCUMENTER_STABLE = "stable";