SALOME Mesh Module

The Mesh module of the SALOME platform integrates mesh engines such as NETGEN, GMSH, and MeshGems. Mesh generation is possible via both GUI operations and Python scripts. Its feature is local control via sub-meshes.

Expressing this with an equation, it becomes like this.

Mesh quality metric:

The numerical solution method of the SALOME Mesh module is based on the Finite Volume Method (FVM) or the Finite Element Method (FEM). Being open-source, its greatest advantage is the ability to check and modify algorithm details at the source code level. Discretization schemes and convergence judgment logic, which are black boxes in commercial solvers, can be directly verified, making it particularly suitable for academic research and method development. Continuous improvement and bug fixes by the community guarantee its quality.

Depending on the type of open-source license (GPL, LGPL, Apache, BSD, etc.), obligations for publishing modified code and restrictions on commercial use differ. It is recommended to check the license conditions before using it in a project and to consult with the company's legal department in advance. Also consider the handling of derivative works and the possibility of dual licensing.

Explains the theoretical foundation of numerical solution methods implemented in open-source CAE tools.

The principle of minimum potential energy, which is the basis of structural analysis:

The displacement field $\mathbf{u}$ that makes $\Pi$ stationary is the equilibrium solution. CalculiX and Code_Aster implement the Galerkin method based on this variational principle.

The FVM adopted by OpenFOAM is based on the integral conservation law for a control volume:

Discrete equations are obtained by applying this integral form to each control volume and numerically evaluating the fluxes on the faces.

Open-source CAE allows third-party verification of algorithms because the source code is public. On the other hand, since there is no vendor support like with commercial tools, information sharing within user communities and forums is important.

• Results from OSS tools should always be verified with known benchmark problems.
• Be aware of incompatibilities between versions (especially differences between forks of OpenFOAM).
• It is recommended to confirm the accuracy of OSS by comparing results with commercial tools.
• When documentation is insufficient, direct reference to the source code may be necessary.

Understanding the dimensionless parameters governing the physical phenomenon being analyzed is the foundation for appropriate model selection and parameter setting.

• Péclet number Pe: Relative importance of convection and diffusion. For Pe >> 1, convection dominates (stabilization methods are needed).
• Reynolds number Re: Ratio of inertial forces to viscous forces. A fundamental parameter for fluid problems.
• Biot number Bi: Ratio of internal conduction to surface convection. For Bi < 0.1, the lumped capacitance method can be applied.
• Courant number CFL: Indicator of numerical stability. For explicit methods, CFL ≤ 1 is required.

For order-of-magnitude estimation of analysis results, dimensional analysis based on Buckingham's Π theorem is effective. Using characteristic length $L$, characteristic velocity $U$, and characteristic time $T = L/U$, estimate the order of each physical quantity in advance to confirm the validity of the analysis results.

Choosing appropriate boundary conditions is directly linked to the uniqueness and physical validity of the solution. Insufficient boundary conditions lead to an ill-posed problem, while excessive ones cause contradictions.

Yeah, you're doing great! Actually moving your hands and trying things is the best way to learn. If you don't understand something, feel free to ask anytime.

The numerical