Hexadominant Mesh
Hexadominant Mesh: Theoretical Foundations
Overview
Teacher! Today's topic is about hexa-dominant mesh, right? What is it like?
A semi-automatic mesh primarily composed of hexahedra. A balance between mesh quality and automation.
Governing Equations
After hearing this, I finally understand why hexa-dominant mesh is important!
Discretization Method
How do you actually solve this equation on a computer?
We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrices 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. higher-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.
Matrix Solver Algorithms
What exactly are matrix solver algorithms?
We solve the system of equations using 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(nยฒ) | Small to Medium Scale |
| Cholesky decomposition | Direct Method (Symmetric Positive Definite) | O(nยฒ) | Small to Medium Scale |
| PCG Method | Iterative Method | O(n) | Large Scale |
| GMRES Method | Iterative Method | O(nยทm) | Large Scale / Non-symmetric |
| AMG Preconditioner | Preprocessing | O(n) | Very Large Scale |
So, if you cut corners in 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 for hexa-dominant meshing?
| 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
Does each software have a dramatic origin story?
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. Features polyhedral meshing.
Current Affiliation: Siemens Digital Industries Software
After hearing this, 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 of development is incredibly 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 regarding the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Especially, higher-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.
I see... Formats may seem simple at first glance, but...
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