Dynamic Mesh (Mesh Deformation)
Theory and Physics
Overview
Teacher! Today's topic is about dynamic mesh (mesh deformation), right? What is it like?
ALE formulation. Introduction of mesh velocity u_g. Spring analogy, diffusion method.
I understand now what my senior meant when they said, "At least do the formulation properly."
Governing Equations
Discretization Methods
How do you actually solve these equations on a computer?
We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.
We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.
Matrix Solution Algorithms
What exactly are matrix solution algorithms?
Solve the simultaneous equations by direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.
| Solver | Classification | Memory Usage | Applicable Scale |
|---|---|---|---|
| LU decomposition | Direct Method | O(n²) | Small to Medium Scale |
| Cholesky decomposition | Direct Method (Symmetric Positive Definite) | O(n²) | Small to Medium Scale |
| PCG Method | Iterative Method | O(n) | Large Scale |
| GMRES method | Iterative Method | O(n·m) | Large Scale / Non-symmetric |
| AMG Preconditioner | Preprocessing | O(n) | Very Large Scale |
So if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!
Implementation in Commercial Tools
So, what software can be used to do dynamic mesh (mesh deformation)?
| Tool Name | Developer/Current | Main File Formats |
|---|---|---|
| Ansys Fluent | Ansys Inc. | .cas, .dat, .msh, .jou |
| Simcenter STAR-CCM+ | Siemens Digital Industries Software | .sim, .java, .csv |
| OpenFOAM | Open Source (OpenCFD/ESI, OpenFOAM Foundation) | Dictionary files (blockMeshDict, etc.), .foam |
| Ansys CFX | Ansys Inc. | .cfx, .def, .res, .ccl |
Vendor Lineage and Product Integration History
Are the origins of each software quite dramatic?
Ansys Fluent
Next is about Ansys Fluent. What's the content?
Developed by Fluent Inc. Acquired by Ansys in 2006. A general-purpose CFD solver based on unstructured grids.
Current Affiliation: Ansys Inc.
Simcenter STAR-CCM+
Next is about Simcenter STAR. What's the content?
Developed by CD-adapco. Acquired by Siemens in 2016 and integrated into the Simcenter brand. Polyhedral mesh is a key feature.
Current Affiliation: Siemens Digital Industries Software
After hearing this far, I finally understand why development is important!
OpenFOAM
What exactly is OpenFOAM?
Open-source CFD originating from Imperial College London. Parallel development by OpenCFD Ltd (under ESI Group) and The OpenFOAM Foundation.
Current Affiliation: Open Source (OpenCFD/ESI, OpenFOAM Foundation)
Wow, the story about development is super interesting! Tell me more.
File Formats and Interoperability
Are there any points to note when transferring data between different software?
| Format | Extension | Type | Overview |
|---|---|---|---|
| CGNS | .cgns | CFD Data | CFD General Notation System. Standard exchange format for CFD results. |
| VTK | .vtk/.vtu | Visualization | Visualization Toolkit format. Used by ParaView, etc. |
| STL | .stl | Mesh | Triangular facets only. 3D printer standard. Not suitable for CAE meshing. |
When converting models between different solvers, attention is needed to the correspondence of element types, compatibility of material models, and differences in the representation of loads/boundary conditions. Especially, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.
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