MMS: Spalart-Allmaras Turbulence Model
MMS: Theoretical Foundations
Overview
Professor! Today's topic is MMS: Spalart-Allmaras Turbulence Model, right? What is it like?
MMS for the SA turbulence model transport equation. Implementation verification of the production term, diffusion term, and near-wall damping.
Governing Equations
I see. So if the turbulence model is properly described, that's a good start, right?
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 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 Algorithm
What exactly do you mean by matrix solution algorithm?
We 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 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 to do MMS: Spalart-Allmaras Turbulence Model?
| Tool Name | Developer/Current | Main File Formats |
|---|---|---|
| MSC Nastran / NX Nastran | MSC Nastran (Hexagon), NX Nastran (Siemens Digital Industries Software) | .bdf, .dat, .f06, .op2, .pch |
| Abaqus FEA (SIMULIA) | Dassault Systèmes SIMULIA | .inp, .odb, .cae, .sta, .msg |
| Ansys Mechanical (formerly ANSYS Structural) | Ansys Inc. | .cdb, .rst, .db, .ans, .mac |
| Ansys Fluent | Ansys Inc. | .cas, .dat, .msh, .jou |
| Simcenter STAR-CCM+ | Siemens Digital Industries Software | .sim, .java, .csv |
| COMSOL Multiphysics | COMSOL AB | .mph |
| OpenFOAM | Open Source (OpenCFD/ESI, OpenFOAM Foundation) | Dictionary files (blockMeshDict, etc.), .foam |
Vendor Lineage and Product Integration History
Is the origin of each software quite dramatic?
MSC Nastran / NX Nastran
Next is about MSC Nastran. What's the story?
Developed in the 1960s as NASA Structural Analysis (NASTRAN). Commercialized by MSC Software, later UGS (now Siemens) derived NX Nastran. MSC was acquired by Hexagon AB in 2017.
Current Affiliation: MSC Nastran (Hexagon), NX Nastran (Siemens Digital Industries Software)
Abaqus FEA (SIMULIA)
What exactly is Abaqus FEA?
Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.
Current Affiliation: Dassault Systèmes SIMULIA
Wait, wait, structural analysis... so can it also be used for cases like this?
Ansys Mechanical (formerly ANSYS Structural)
Tell me about "Ansys Mechanical"!
Developed in 1970 by Swanson Analysis Systems Inc. (SASI). Based on APDL (Ansys Parametric Design Language).
Current Affiliation: Ansys Inc.
Wow, the structural analysis story 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 |
|---|---|---|---|
| STEP | .stp/.step | 3D Geometry | International standard for 3D CAD geometry exchange. Widely supported. Best for surface and solid geometry transfer. |
| IGES | .igs/.iges | 3D Geometry | Older 3D geometry exchange format. Legacy standard. Support varies by software. |
| STL | .stl | 3D Mesh | Stereolithography format. Stores surface mesh as triangles. Widely used for 3D printing and CFD preprocessing. |
| Nastran BDF | .bdf/.dat | FEM Model | Nastran bulk data format. Stores mesh, elements, material properties, boundary conditions. Native to Nastran family. |
| Abaqus INP | .inp | FEM Model | Abaqus input file format. Defines geometry, mesh, material, and loads. Human-readable text format. |
| ANSYS CDB | .cdb | FEM Model | ANSYS database file. Native format for Mechanical. Contains full model including mesh, loads, and boundary conditions. |
| Fluent Case | .cas/.case | CFD Model | Fluent native format. Stores mesh, domain, boundary conditions, and solution data. |
| Fluent Mesh | .msh | CFD Mesh | Fluent native mesh format. Pure mesh without solution. Can be exported to other CFD codes. |
| OpenFOAM | Dictionary | CFD Model | Text-based dictionary format. Highly customizable and human-readable. |