OpenFOAM入門

OpenFOAM is a C++-based open-source CFD toolkit, centered on fluid analysis using the Finite Volume Method (FVM), and provides a wide range of physical models. There are two main branches: the ESI version and the Foundation version.

Expressing this with equations, it looks like this.

Finite Volume Method discretization:

The numerical methods for the introduction to OpenFOAM are based on the Finite Volume Method (FVM) or the Finite Element Method (FEM). Being open-source, its greatest advantage is the ability to inspect and modify algorithm details at the source code level. Discretization schemes and convergence criteria 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 ensure its quality.

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

The principle of minimum potential energy, which is the foundation 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.

Because the source code is public, open-source CAE allows third-party verification of algorithms. 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 version incompatibilities (especially differences between OpenFOAM forks).
• It is recommended to confirm OSS accuracy by comparing results with commercial tools.
• When documentation is lacking, 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.

• Peclet Number Pe: Relative importance of convection and diffusion. For Pe >> 1, convection dominates (stabilization techniques are required).
• 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 is applicable.
• Courant Number CFL: Indicator of numerical stability. For explicit methods, CFL ≤ 1 is required.

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

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

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

Explains the key points of numerical methods and implementation for the introduction to OpenFOAM.

Building from source code uses CMake or dedicated build systems (like OpenFOAM's wmake). Proper version management of dependency libraries (MPI, PETSc, BLAS/LAPACK, etc.) is crucial. A Linux environment is recommended, but using WSL2 or Docker containers makes it possible to set up on Windows as well.