CSS Surface Tension Model

.github/workflows/Documenter.yml

@@ -17,8 +17,6 @@ on:
   workflow_dispatch:
 
 concurrency:
-  # Skip intermediate builds: always.
-  # Cancel intermediate builds: only if it is a pull request build.
   group: ${{ github.workflow }}-${{ github.ref }}
   cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
 

NEWS.md

@@ -3,51 +3,85 @@
 TrixiParticles.jl follows the interpretation of [semantic versioning (semver)](https://julialang.github.io/Pkg.jl/dev/compatibility/#Version-specifier-format-1)
 used in the Julia ecosystem. Notable changes will be documented in this file for human readability.
 
+## Version 0.2.4
+
+### Features
+
+- Support for surface tension was added to EDAC (#539)
+- A method to prevent penetration of fast moving particles with solids was added (#498)
+- Added the callback `SteadyStateReachedCallback` to detect convergence of static simulations (#601)  
+- Added Ideal Gas State Equation (#607)
+
+### Documentation
+
+- GPU Support Documentation was added (#660)
+- A new user tutorial was added (#514)
+
+### Fixes
+
+- Diverse Doc fixes (#663, #659, #637, #658, #664)
+- Simulations can be run with `Float32` (#662)
+
+### Refactored
+
+- Surface normal calculation was moved from surface_tension.jl to surface_normal_sph.jl (#539)
+
 ## Version 0.2.3
 
 ### Highlights
+
 Transport Velocity Formulation (TVF) based on the work of Ramachandran et al. "Entropically damped artificial compressibility for SPH" (2019) was added.
 
 ## Version 0.2.2
 
 ### Highlights
+
 Hotfix for threaded sampling of complex geometries.
 
 ## Version 0.2.1
 
 ### Highlights
+
 Particle sampling of complex geometries from `.stl` and `.asc` files.
 
 ## Version 0.2.0
 
 ### Removed
+
 Use of the internal neighborhood search has been removed and replaced with PointNeighbors.jl.
 
 ## Development Cycle 0.1
 
 ### Highlights
 
 #### Discrete Element Method
+
 A basic implementation of the discrete element method was added.
 
 #### Surface Tension and Adhesion Model
+
 A surface tension and adhesion model based on the work by Akinci et al., "Versatile Surface Tension and Adhesion for SPH Fluids" (2013) was added to WCSPH.
 
 #### Support for Open Boundaries
+
 Open boundaries using the method of characteristics based on the work of Lastiwka et al., "Permeable and non-reflecting boundary conditions in SPH" (2009) were added for WCSPH and EDAC.
 
 ## Pre Initial Release (v0.1.0)
+
 This section summarizes the initial features that TrixiParticles.jl was released with.
 
 ### Highlights
 #### EDAC
+
 An implementation of EDAC (Entropically Damped Artificial Compressibility) was added,
 which allows for more stable simulations compared to basic WCSPH and reduces spurious pressure oscillations.
 
 #### WCSPH
+
 An implementation of WCSPH (Weakly Compressible Smoothed Particle Hydrodynamics), which is the classical SPH approach.
 
 Features:
+
 - Correction schemes (Shepard (0. Order) ... MixedKernelGradient (1. Order))
 - Density reinitialization
 - Kernel summation and Continuity equation density formulations
@@ -57,4 +91,5 @@ Features:
 
 
 #### TLSPH
+
 An implementation of TLSPH (Total Lagrangian Smoothed Particle Hydrodynamics) for solid bodies enabling FSI (Fluid Structure Interactions).

Project.toml

@@ -1,7 +1,7 @@
 name = "TrixiParticles"
 uuid = "66699cd8-9c01-4e9d-a059-b96c86d16b3a"
 authors = ["erik.faulhaber <[email protected]>"]
-version = "0.2.4-dev"
+version = "0.2.4"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"

docs/make.jl

@@ -139,8 +139,8 @@ makedocs(sitename="TrixiParticles.jl",
                      "Util" => joinpath("general", "util.md")
                  ],
                  "Systems" => [
-                     "Discrete Element Method (Solid)" => joinpath("systems",
-                                                                   "dem.md"),
+                     "Fluid Models" => joinpath("systems", "fluid.md"),
+                     "Discrete Element Method (Solid)" => joinpath("systems", "dem.md"),
                      "Weakly Compressible SPH (Fluid)" => joinpath("systems",
                                                                    "weakly_compressible_sph.md"),
                      "Entropically Damped Artificial Compressibility for SPH (Fluid)" => joinpath("systems",

docs/src/refs.bib

@@ -329,6 +329,19 @@ @Article{Hormann2001
   publisher = {Elsevier BV},
 }
 
+@Article{Huber2016,
+  title = {On the physically based modeling of surface tension and moving contact lines with dynamic contact angles on the continuum scale},
+  journal = {Journal of Computational Physics},
+  volume = {310},
+  pages = {459-477},
+  year = {2016},
+  issn = {0021-9991},
+  doi = {https://doi.org/10.1016/j.jcp.2016.01.030},
+  url = {https://www.sciencedirect.com/science/article/pii/S0021999116000383},
+  author = {M. Huber and F. Keller and W. Säckel and M. Hirschler and P. Kunz and S.M. Hassanizadeh and U. Nieken},
+  keywords = {SPH, Two-phase flow, Surface tension, Moving contact line, Dynamic contact angle, CSF, CLF}
+}
+
 
 @Article{Jacobson2013,
   author    = {Jacobson, Alec and Kavan, Ladislav and Sorkine-Hornung, Olga},
@@ -491,6 +504,19 @@ @Article{Morris1997
   publisher = {Elsevier BV},
 }
 
+@article{Morris2000,
+  author = {Morris, Joseph P.},
+  title = {Simulating surface tension with smoothed particle hydrodynamics},
+  journal = {International Journal for Numerical Methods in Fluids},
+  volume = {33},
+  number = {3},
+  pages = {333-353},
+  keywords = {interfacial flow, meshless methods, surface tension},
+  doi = {https://doi.org/10.1002/1097-0363(20000615)33:3<333::AID-FLD11>3.0.CO;2-7},
+  year = {2000}
+}
+
+
 @InProceedings{Mueller2003,
   author    = {M{\"u}ller, Matthias and Charypar, David and Gross, Markus},
   booktitle = {Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation},

docs/src/systems/fluid.md

@@ -0,0 +1,212 @@
+
+# [Fluid Models](@id fluid_models)
+Currently available fluid methods are the [weakly compressible SPH method](@ref wcsph) and the [entropically damped artificial compressibility for SPH](@ref edac).  
+This page lists models and techniques that apply to both of these methods.  
+
+## [Viscosity](@id viscosity_wcsph)
+
+TODO: Explain viscosity.
+
+```@autodocs
+Modules = [TrixiParticles]
+Pages = [joinpath("schemes", "fluid", "viscosity.jl")]
+```
+
+## [Corrections](@id corrections)
+
+```@autodocs
+Modules = [TrixiParticles]
+Pages = [joinpath("general", "corrections.jl")]
+```
+
+
+---
+
+## [Surface Normals](@id surface_normal)
+
+### Overview of Surface Normal Calculation in SPH
+
+Surface normals are essential for modeling surface tension as they provide the directionality of forces acting at the fluid interface. They are calculated based on the particle properties and their spatial distribution within the smoothed particle hydrodynamics (SPH) framework.
+
+#### Color Field and Gradient-Based Surface Normals
+
+The surface normal at a particle is derived from the color field, a scalar field assigned to particles to distinguish between different fluid phases or between fluid and air. The color field gradients point towards the interface, and the normalized gradient defines the surface normal direction.
+
+The simplest SPH formulation for surface normal, \( n_a \), is given as:
+```math
+n_a = \sum_b m_b \frac{c_b}{\rho_b} \nabla_a W_{ab},
+```
+where:
+- \( c_b \) is the color field value for particle \( b \),
+- \( m_b \) is the mass of particle \( b \),
+- \( \rho_b \) is the density of particle \( b \),
+- \( \nabla_a W_{ab} \) is the gradient of the smoothing kernel \( W_{ab} \) with respect to particle \( a \).
+
+#### Normalization of Surface Normals
+
+The calculated normals are normalized to unit vectors:
+```math
+\hat{n}_a = \frac{n_a}{\Vert n_a \Vert}.
+```
+Normalization ensures that the magnitude of the normals does not bias the curvature calculations or the resulting surface tension forces.
+
+#### Handling Noise and Errors in Normal Calculation
+
+In regions distant from the interface, the calculated normals may be small or inaccurate due to the smoothing kernel's support radius. To mitigate this:
+1. Normals below a threshold are excluded from further calculations.
+2. Curvature calculations use a corrected formulation to reduce errors near interface fringes.
+
+```@autodocs
+Modules = [TrixiParticles]
+Pages = [joinpath("schemes", "fluid", "surface_normal_sph.jl")]
+```
+
+---
+
+## [Surface Tension](@id surface_tension)
+
+### Introduction to Surface Tension in SPH
+
+Surface tension is a key phenomenon in fluid dynamics, influencing the behavior of droplets, bubbles, and fluid interfaces. In SPH, surface tension is modeled as forces arising due to surface curvature and particle interactions, ensuring realistic simulation of capillary effects, droplet coalescence, and fragmentation.
+
+### Akinci-Based Intra-Particle Force Surface Tension and Wall Adhesion Model
+
+The Akinci model divides surface tension into distinct force components:
+
+#### Cohesion Force
+
+The cohesion force captures the attraction between particles at the fluid interface, creating the effect of surface tension. It is defined by the distance between particles and the support radius \( h_c \), using a kernel-based formulation.
+
+**Key Features:**
+- Particles within half the support radius experience a repulsive force to prevent clustering.
+- Particles beyond half the radius but within the support radius experience an attractive force to simulate cohesion.
+
+Mathematically:
+```math
+F_{\text{cohesion}} = -\sigma m_b C(r) \frac{r}{\Vert r \Vert},
+```
+where \( C(r) \), the cohesion kernel, is defined as:
+```math
+C(r)=\frac{32}{\pi h_c^9}
+\begin{cases}
+(h_c-r)^3 r^3, & \text{if } 2r > h_c, \\
+2(h_c-r)^3 r^3 - \frac{h^6}{64}, & \text{if } r > 0 \text{ and } 2r \leq h_c, \\
+0, & \text{otherwise.}
+\end{cases}
+```
+
+#### Surface Area Minimization Force
+
+The surface area minimization force models the curvature reduction effects, aligning particle motion to reduce the interface's total area. It acts based on the difference in surface normals:
+```math
+F_{\text{curvature}} = -\sigma (n_a - n_b),
+```
+where \( n_a \) and \( n_b \) are the surface normals of the interacting particles.
+
+#### Wall Adhesion Force
+
+This force models the interaction between fluid and solid boundaries, simulating adhesion effects at walls. It uses a custom kernel with a peak at 0.75 times the support radius:
+```math
+F_{\text{adhesion}} = -\beta m_b A(r) \frac{r}{\Vert r \Vert},
+```
+where \( A(r) \) is the adhesion kernel:
+```math
+A(r) = \frac{0.007}{h_c^{3.25}}
+\begin{cases}
+\sqrt[4]{-\frac{4r^2}{h_c} + 6r - 2h_c}, & \text{if } 2r > h_c \text{ and } r \leq h_c, \\
+0, & \text{otherwise.}
+\end{cases}
+```
+
+---
+
+### Morris-Based Momentum-Conserving Surface Tension Model
+
+In addition to the Akinci model, Morris (2000) introduced a momentum-conserving approach to surface tension. This model uses stress tensors to ensure exact conservation of linear momentum, providing a robust method for high-resolution simulations.
+
+#### Stress Tensor Formulation
+
+The force is calculated as:
+```math
+F_{\text{surface tension}} = \nabla \cdot S,
+```
+where \( S \) is the stress tensor:
+```math
+S = \sigma \delta_s (I - \hat{n} \otimes \hat{n}),
+```
+with:
+- \( \delta_s \): Surface delta function,
+- \( \hat{n} \): Unit normal vector,
+- \( I \): Identity matrix.
+
+#### Advantages and Limitations
+
+While momentum conservation makes this model attractive, it requires additional computational effort and stabilization techniques to address instabilities in high-density regions.
+
+# [Huber Model](@id huber_model)
+
+## Introduction to the Huber Contact Force Model
+
+The **Huber Model**, introduced in [Huber2016](@cite), provides a physically-based approach for simulating surface tension and contact line dynamics in Smoothed Particle Hydrodynamics (SPH). It is specifically designed to address challenges in modeling wetting phenomena, including dynamic contact angles and their influence on fluid behavior.
+
+The Huber Model introduces a **Contact Line Force (CLF)** that complements the **Continuum Surface Force (CSF)** model, allowing for accurate representation of fluid-fluid and fluid-solid interactions. The dynamic evolution of contact angles emerges naturally from the force balance without requiring artificial adjustments or fitting parameters.
+
+---
+
+## Key Features of the Huber Model
+
+1. **Dynamic Contact Angles**:
+   - Captures the transition between static and dynamic contact angles based on interfacial forces and contact line velocities.
+   - Removes the need for predefined constitutive equations, as the contact angle is derived from the system's dynamics.
+
+2. **Volume Reformulation**:
+   - Transforms line-based forces (e.g., those acting at the contact line) into volume-based forces for compatibility with SPH formulations.
+   - Ensures smooth force distribution near the contact line, reducing numerical artifacts.
+
+3. **Momentum Balance**:
+   - Extends the Navier-Stokes equations to include contributions from the contact line, ensuring accurate modeling of wetting and spreading dynamics.
+
+4. **No Fitting Parameters**:
+   - Fully physics-driven, requiring only measurable inputs like surface tension coefficients and static contact angles.
+
+---
+
+## Mathematical Formulation
+
+### Contact Line Force (CLF)
+
+The force acting along the contact line is derived from the unbalanced Young Force:
+```math
+f_{\text{CLF}} = \sigma_{\text{wn}} [\cos(\alpha_s) - \cos(\alpha_d)] \hat{\nu},
+```
+where:
+- \( \sigma_{\text{wn}} \): Surface tension coefficient of the fluid-fluid interface,
+- \( \alpha_s \): Static contact angle,
+- \( \alpha_d \): Dynamic contact angle,
+- \( \hat{\nu} \): Tangential unit vector along the fluid-solid interface.
+
+### Volume Reformulation
+
+To incorporate the CLF into SPH, it is reformulated as a volume force:
+```math
+F_{\text{CLF}} = f_{\text{CLF}} \delta_{\text{CL}},
+```
+where \( \delta_{\text{CL}} \) is a Dirac delta function approximated by SPH kernels, ensuring the force is applied locally near the contact line.
+
+---
+
+## Applications
+
+1. **Droplet Dynamics**:
+   - Simulates droplet spreading, recoiling, and merging with accurate contact line evolution.
+
+2. **Capillary Action**:
+   - Models fluid behavior in porous media and confined geometries, where contact lines play a critical role.
+
+3. **Wetting Phenomena**:
+   - Predicts equilibrium shapes and transient states of droplets and films on solid surfaces.
+
+```@autodocs
+Modules = [TrixiParticles]
+Pages = [joinpath("schemes", "fluid", "surface_tension.jl")]
+```