thermal tutorial

doc/tutorials/120-mazes/README.md

@@ -9,6 +9,9 @@ number-sections: true
 toc: true
 prev_link: ../110-tensile-test
 prev_title: \#1 Tensile test
+next_link: ../320-thermal
+next_title: \#3 Heat conduction
+
 ...
 
 

doc/tutorials/320-thermal/.gitignore

@@ -0,0 +1,3 @@
+README.pdf
+*.vtk
+*.msh

doc/tutorials/320-thermal/README.markdown

@@ -0,0 +1,164 @@
+# FeenoX Tutorial \#3: Heat conduction
+
+- [<span class="toc-section-number">1</span> Foreword][]
+  - [<span class="toc-section-number">1.1</span> Summary][]
+- [<span class="toc-section-number">2</span> Linear steady-state
+  problems][]
+  - [<span class="toc-section-number">2.1</span> Temperature
+    conditions][]
+    - [<span class="toc-section-number">2.1.1</span> Single-material
+      slab][]
+    - [<span class="toc-section-number">2.1.2</span> Two-material
+      slab][]
+  - [<span class="toc-section-number">2.2</span> Heat flux conditions][]
+  - [<span class="toc-section-number">2.3</span> Convection
+    conditions][]
+  - [<span class="toc-section-number">2.4</span> Volumetric heat
+    sources][]
+  - [<span class="toc-section-number">2.5</span> Space-dependent
+    properties: manufactured solution][]
+- [<span class="toc-section-number">3</span> Non-linear state-state
+  problems][]
+  - [<span class="toc-section-number">3.1</span> Temperature-dependent
+    heat flux: radiation][]
+  - [<span class="toc-section-number">3.2</span> Temperature-dependent
+    conductivity][]
+  - [<span class="toc-section-number">3.3</span> Temperature-dependent
+    sources][]
+- [<span class="toc-section-number">4</span> Transient problems][]
+  - [<span class="toc-section-number">4.1</span> From an arbitrary
+    initial condition][]
+  - [<span class="toc-section-number">4.2</span> From a steady state][]
+
+  [<span class="toc-section-number">1</span> Foreword]: #sec:foreword
+  [<span class="toc-section-number">1.1</span> Summary]: #summary
+  [<span class="toc-section-number">2</span> Linear steady-state problems]:
+    #linear-steady-state-problems
+  [<span class="toc-section-number">2.1</span> Temperature conditions]: #temperature-conditions
+  [<span class="toc-section-number">2.1.1</span> Single-material slab]: #single-material-slab
+  [<span class="toc-section-number">2.1.2</span> Two-material slab]: #two-material-slab
+  [<span class="toc-section-number">2.2</span> Heat flux conditions]: #heat-flux-conditions
+  [<span class="toc-section-number">2.3</span> Convection conditions]: #convection-conditions
+  [<span class="toc-section-number">2.4</span> Volumetric heat sources]:
+    #volumetric-heat-sources
+  [<span class="toc-section-number">2.5</span> Space-dependent properties: manufactured solution]:
+    #space-dependent-properties-manufactured-solution
+  [<span class="toc-section-number">3</span> Non-linear state-state problems]:
+    #non-linear-state-state-problems
+  [<span class="toc-section-number">3.1</span> Temperature-dependent heat flux: radiation]:
+    #temperature-dependent-heat-flux-radiation
+  [<span class="toc-section-number">3.2</span> Temperature-dependent conductivity]:
+    #temperature-dependent-conductivity
+  [<span class="toc-section-number">3.3</span> Temperature-dependent sources]:
+    #temperature-dependent-sources
+  [<span class="toc-section-number">4</span> Transient problems]: #transient-problems
+  [<span class="toc-section-number">4.1</span> From an arbitrary initial condition]:
+    #from-an-arbitrary-initial-condition
+  [<span class="toc-section-number">4.2</span> From a steady state]: #from-a-steady-state
+
+# Foreword
+
+Welcome to **FeenoX’s tutorial number three**. Here you will learn how
+to solve the heat conduction equation with FeenoX in all of its flavors:
+linear and non-linear, static and transient.
+
+## Summary
+
+- We start solving steady-state problems. As long as neither of the
+
+  1.  material properties, nor
+  2.  sources
+
+  depend on the temperature $T(\vec{x})$ and
+
+  3.  the boundary conditions do not depend or depend linearly
+      on $T(\vec{x})$
+
+  then problem is linear. If these three guys depend on space $\vec{x}$
+  (but not on $T(\vec{x})$, the problem is still linear:
+
+  ``` feenox
+  ```
+
+- If any of a. b. or c. do depend on the temperature $T(\vec{x})$, then
+  the problem is non-linear. FeenoX is able to detect this and will
+  switch to a non-linear solver automatically. You can check this by
+  passing `--snes_view` in the command line. Here, SNES means “Scalable
+  Non-linear Equation Solvers” in PETSc’s jargon. The `--snes_view`
+  option will show some details about the solver. In linear problems,
+  SNES is not used but the KSP (Krylov SubSpace solvers) framework is
+  used instead. Therefore, `--snes_view` is empty for linear problems.
+
+- We show how to trigger non-linearities by
+
+  - adding a boundary conditions that depends on $T(\vec{x})$, such as
+    radiation
+  - having a conductivity that depends on temperature, which is the case
+    for most materials anyway
+  - using heat sources that are temperature-dependent, where
+    increasing $T$ decreases the source
+
+- Finally we show how to solve transient problems, either
+
+  1.  starting from an arbitrary initial temperature distribution using
+      constant boundary conditions
+  2.  starting from a steady-state solution and changing the boundary
+      conditions over time
+  3.  both
+
+# Linear steady-state problems
+
+In this section we are going to ask FeenoX to compute a temperature
+distribution $T(\vec{x})$ that satisfies
+
+$$
+- \text{div} \Big[ k(\vec{x}) \cdot \text{grad} T(\vec{x}) \Big] = q(\vec{x})
+$$
+
+## Temperature conditions
+
+### Single-material slab
+
+### Two-material slab
+
+## Heat flux conditions
+
+These problems need at least one fixed-temperature (a.k.a. Dirichlet)
+condition.
+
+## Convection conditions
+
+## Volumetric heat sources
+
+## Space-dependent properties: manufactured solution
+
+# Non-linear state-state problems
+
+The initial guess is given with `T_guess(x,y,z)` (or `T_guess(x,y)` or
+`T_guess(x)`).
+
+## Temperature-dependent heat flux: radiation
+
+Mind the units! Kelvin:
+
+Celsius:
+
+## Temperature-dependent conductivity
+
+UO$_2$
+
+## Temperature-dependent sources
+
+[Le Chatelier’s principle][]
+
+  [Le Chatelier’s principle]: https://en.wikipedia.org/wiki/Le_Chatelier's_principle
+
+# Transient problems
+
+## From an arbitrary initial condition
+
+UO$_2$
+
+## From a steady state
+
+Pump

doc/tutorials/320-thermal/README.md

@@ -0,0 +1,108 @@
+---
+title: Heat conduction
+subtitle: FeenoX Tutorial \#3
+titleblock: |
+ FeenoX Tutorial \#3: Heat conduction
+ ====================================
+lang: en-US
+number-sections: true
+toc: true
+prev_link: ../120-mazes
+prev_title: \#2 Solving mazes
+...
+
+# Summary
+
+Welcome to **FeenoX’s tutorial number three**.
+Here you will learn how to solve the heat conduction equation with FeenoX in all of its flavors: linear and non-linear, static and transient.
+
+
+ * We start solving steady-state problems. As long as neither of the
+
+    a. material properties, nor
+    b. sources
+
+   depend on the temperature $T(\vec{x})$ and 
+
+    c. the boundary conditions do not depend or depend linearly on $T(\vec{x})$
+
+   then problem is linear.
+   If these three guys depend on space $\vec{x}$ (but not on $T(\vec{x})$), the problem is still linear no matter how complex it looks like:
+
+   ```{.feenox include="manufactured.fee"}
+   ```
+
+ * If any of a. b. or c. do depend on the temperature $T(\vec{x})$, then the problem is non-linear.
+   FeenoX is able to detect this and will switch to a non-linear solver automatically.
+   You can check this by passing `--snes_view` in the command line. Here, SNES means "Scalable Non-linear Equation Solvers" in PETSc's jargon. The `--snes_view` option will show some details about the solver. In linear problems, SNES is not used but the KSP (Krylov SubSpace solvers) framework is used instead. Therefore, `--snes_view` is empty for linear problems. 
+
+ * We show how to trigger non-linearities by
+
+    - adding a boundary conditions that depends on $T(\vec{x})$, such as radiation
+    - having a conductivity that depends on temperature, which is the case for most materials anyway
+    - using heat sources that are temperature-dependent, where increasing $T$ decreases the source
+
+ * Finally we show how to solve transient problems, either
+
+    i. starting from an arbitrary initial temperature distribution using constant boundary conditions
+    ii. starting from a steady-state solution and changing the boundary conditions over time
+    iii. both
+
+# Linear steady-state problems
+
+In this section we are going to ask FeenoX to compute a temperature distribution $T(\vec{x})$ that satisfies 
+
+$$
+- \text{div} \Big[ k(\vec{x}) \cdot \text{grad} \left[ T(\vec{x}) \right] \Big] = q(\vec{x})
+$$
+
+along with proper boundary conditions.
+
+
+## Temperature conditions
+
+### Single-material slab
+
+### Two-material slab
+
+## Heat flux conditions
+
+These problems need at least one fixed-temperature (a.k.a. Dirichlet) condition.
+
+## Convection conditions
+
+## Volumetric heat sources
+
+## Space-dependent properties: manufactured solution
+
+
+# Non-linear state-state problems
+
+The initial guess is given with `T_guess(x,y,z)` (or `T_guess(x,y)` or `T_guess(x)`).
+
+## Temperature-dependent heat flux: radiation
+
+Mind the units!
+Kelvin:
+
+Celsius:
+
+## Temperature-dependent conductivity
+
+UO$_2$
+
+## Temperature-dependent sources
+
+[Le Chatelier's principle](https://en.wikipedia.org/wiki/Le_Chatelier's_principle)
+
+
+# Transient problems
+
+## From an arbitrary initial condition
+
+UO$_2$
+
+## From a steady state
+
+Pump
+

doc/tutorials/320-thermal/clean.sh

@@ -0,0 +1 @@
+cat .gitignore | sed '/^#.*/ d' | sed '/^\s*$/ d' | sed 's/^/rm -rf /' | grep -v mp4 | bash

doc/tutorials/320-thermal/manufactured.fee

@@ -0,0 +1,20 @@
+PROBLEM thermal 2D
+READ_MESH square.msh
+
+T_manufactured(x,y) = 1 + sin(2*x)^2 * cos(3*y)^2
+k(x,y) = 1 + x - 0.5*y
+
+VAR x' x'' y' y''
+q(x,y) = -(derivative(k(x',y) * derivative(T_manufactured(x'',y), x'', x'), x', x) + \
+           derivative(k(x,y') * derivative(T_manufactured(x,y''), y'', y'), y', y))
+
+BC left   T=T_manufactured(x,y)
+BC top    T=T_manufactured(x,y)
+BC bottom q=+(-k(x,y)*derivative(T_manufactured(x,y'),y',y))
+BC right  q=-(-k(x,y)*derivative(T_manufactured(x',y),x',x))
+
+SOLVE_PROBLEM
+
+WRITE_MESH manufactured.vtk T T_manufactured T(x,y)-T_manufactured(x,y)
+INTEGRATE (T(x,y)-T_manufactured(x,y))^2 RESULT e2
+PRINT e2

doc/tutorials/320-thermal/square.geo

@@ -0,0 +1,11 @@
+SetFactory("OpenCASCADE");
+Rectangle(1) = {0, 0, 0, 1, 1, 0};
+
+Physical Surface("bulk", 1) = {1};
+Physical Curve("left", 2) = {4};
+Physical Curve("right", 3) = {2};
+Physical Curve("bottom", 4) = {1};
+Physical Curve("top", 5) = {3};
+
+Mesh.MeshSizeMax = 1/10;
+

doc/tutorials/320-thermal/syntax-feenox.tex

@@ -0,0 +1 @@
+../../syntax-feenox.tex

doc/tutorials/320-thermal/syntax.tex

@@ -0,0 +1 @@
+../../syntax.tex

doc/tutorials/README.markdown

@@ -21,11 +21,12 @@ discussed in the [documentation][], particularly in the
 As such, it is a tool that in principle should be used from a
 higher-level interface (e.g. a web-based UI such as \<www.caeplex.com\>)
 or called from a set of automated scripts following some kind of
-parametric or optimization workflow. In any case, if you want to learn
-how to create your web-based interface or how to implement an
-optimization workflow on your own, you will need to start running simple
-cases manually and then increasing the complexity until reaching the
-solve state-of-the-art capabilities.
+parametric or optimization workflow.
+
+In any case, if you want to learn how to create your web-based interface
+or how to implement an optimization workflow on your own, you will need
+to start running simple cases manually and then increasing the
+complexity until reaching the solve state-of-the-art capabilities.
 
 Recall by reading again the [project’s main README][], that FeenoX is—in
 a certain sense—to desktop FEA programs (like [Code_Aster][] with
@@ -80,9 +81,11 @@ since it is [free and open source software][].
 # Physics tutorials
 
 1.  The Laplace equation
-2.  Heat conduction
+2.  [Heat conduction][]
 3.  Linear elasticity
 4.  Modal analysis
 5.  Thermo-mechanical analysis
 6.  Neutron diffusion
 7.  Neutron transport
+
+  [Heat conduction]: 320-thermal

doc/tutorials/README.md

@@ -37,7 +37,7 @@ general.md
 # Physics tutorials
 
  1. The Laplace equation
- 2. Heat conduction
+ 2. [Heat conduction](320-thermal)
  3. Linear elasticity
  4. Modal analysis
  5. Thermo-mechanical analysis

doc/tutorials/make.sh

@@ -1,5 +1,5 @@
 #!/bin/bash -e
-for i in . 000-setup 110-tensile-test 120-mazes; do
+for i in . 000-setup 110-tensile-test 120-mazes 320-thermal; do
   ../md2.sh --pdf  ${i}/README
   ../md2.sh --gfm  ${i}/README
   ../md2.sh --html ${i}/README