CalculiX Linear Static Analysis
CalculiX Linear Static Analysis: Theoretical Foundations
(CalculiX Linear Static Analysis: Theoretical Foundations Section)
Computational Methods for CalculiX Linear Static Analysis
Details of Numerical Methods
Specifically, what algorithm is used to solve CalculiX linear static analysis?
Let me explain the key points of the numerical solution method and implementation for CalculiX linear static analysis.
Wow, the talk about numerical methods for linear static analysis is super interesting! Please tell me more.
Compilation and Build
I've heard of "compilation and build," but I might not fully understand it...
So, cutting corners during the build from source part will come back to bite you later. I'll keep that in mind!
Input File Structure
Are there any points to be careful about when transferring data between different software?
Understanding the case file structure and major parameter settings is the first step in implementation. The format of dictionary files (dict) and command files is specific to each software, and editing from official tutorial templates is efficient.
Script Automation
I've heard of "script automation," but I might not fully understand it...
Automating parameter studies with Python or Bash scripts is key to improving productivity. You should also consider utilizing wrapper tools like PyFoam and cfMesh.
Debugging and Development Environment
Memory leak detection and debugging with GDB, Valgrind, and AddressSanitizer are effective. Utilize the remote debugging features of IDEs (VSCode, CLion) to set up an efficient development environment. Introduce unit testing frameworks (Google Test, pytest) to automate regression testing.
Solver Settings and Algorithms
I want to know a bit more about what's happening behind the scenes of the calculation!
OpenFOAM Solver Selection Guidelines
What exactly do you mean by solver selection guidelines?
| Solver | Application | Equation System |
|---|---|---|
| simpleFoam | Steady incompressible turbulence | SIMPLE |
| pimpleFoam | Unsteady incompressible | PIMPLE (PISO+SIMPLE) |
| interFoam | Two-phase flow (VOF) | MULES |
| rhoSimpleFoam | Steady compressible | SIMPLE |
| buoyantSimpleFoam | Natural Convection | SIMPLE+Boussinesq |
| reactingFoam | Combustion | PIMPLE+Chemical Reaction |
CalculiX Input File Structure
What exactly do you mean by input file structure?
```
*NODE
1, 0.0, 0.0, 0.0
...
*ELEMENT, TYPE=C3D8
1, 1, 2, 3, 4, 5, 6, 7, 8
...
*MATERIAL, NAME=STEEL
*ELASTIC
210000., 0.3
*DENSITY
7.85e-9
*BOUNDARY
1, 1, 3
*CLOAD
100, 2, 1000.
Ah, I see! So that's how the solver selection guidelines work.
Code_Aster Command File Structure
Next is the talk about command file structure. What's it about?
```
DEBUT()
MAIL = LIRE_MAILLAGE()
MODELE = AFFE_MODELE(MAILLAGE=MAIL, ...)
RESULT = MECA_STATIQUE(MODELE=MODELE, ...)
FIN()
```
Discretization Scheme Selection
Please tell me about "Discretization Scheme Selection"!
OpenFOAM's discretization schemes are set in the fvSchemes file. The discretization of the convection term greatly affects accuracy and stability:
After hearing this, I finally understand why solver selection guidelines are so important!
- upwind: 1st order accuracy, stable but large numerical diffusion
- linearUpwind: 2nd order accuracy, limited
- limitedLinear: 2nd order accuracy, TVD limited
- LUST: blended scheme, recommended for LES
Error Evaluation and Accuracy Verification
I've heard of "error evaluation and accuracy verification," but I might not fully understand it...
Discretization Error Evaluation
What exactly do you mean by discretization error evaluation?
Estimation of discretization error using Richardson extrapolation:
Here, $f_h$ is the solution at mesh width $h$, $r$ is the mesh ratio, and $p$ is the order of discretization.
GCI (Grid Convergence Index)
Please tell me about "GCI"!
Quantitative evaluation of mesh convergence based on ASME V&V 20-2009:
After hearing this, I finally understand why discretization error evaluation is so important!
Expressing this in a formula gives us this.
Hmm, just the formula doesn't click... What does it represent?
Safety factor $F_s = 1.25$ (when comparing three or more mesh levels). GCI < 5% is a guideline for convergence.
Now I understand what my senior meant when he said, "Make sure you properly evaluate discretization error."
Verification Benchmark Problems
Please tell me about "Verification Benchmark Problems"!
To ensure the reliability of analysis results, comparison with the following benchmark problems is recommended:
| Field | Benchmark | Reference Solution |
|---|