OpenFOAM並列計算

Domain decomposition via decomposeParDict (scotch, hierarchical, simple, etc.) and MPI parallel execution setup methods. Scalability optimization and load balancing.

Expressing this with equations, it looks like this.

Amdahl's Law:

The numerical methods for OpenFOAM parallel computing are based on the Finite Volume Method (FVM) or the Finite Element Method (FEM). Being open source, its greatest advantage is the ability to verify 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.

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 terms before using it in a project and consult with the internal legal department in advance. Also consider the handling of derivative works and the possibility of dual licensing.

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

The principle of minimum potential energy, fundamental to 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 OpenFOAM forks).
• It is recommended to verify the accuracy of OSS 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. Pe >> 1 indicates convection dominance (stabilization methods 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. Bi < 0.1 allows application of the lumped capacitance method.
• Courant Number CFL: Indicator of numerical stability. Explicit methods require CFL ≤ 1.

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 in advance 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 hands-on is the best way to learn. If you have any questions, feel free to ask anytime.

Explains the key points of numerical methods and implementation for OpenFOAM parallel computing.

Building from source code uses CMake or dedicated build systems (like OpenFOAM's wmake). Dependency libraries (MPI, PETSc, etc.) must be installed in advance. For production environments, it is recommended to use pre-built binaries or container images (Docker, Singularity) to ensure reproducibility.

OpenFOAM's parallel computing is based on domain decomposition. The decomposeParDict file specifies the decomposition method (scotch, hierarchical, simple, etc.) and the number of subdomains. The decomposed mesh and fields are distributed to each processor, and calculations proceed with communication of boundary information (ghost cells).

Parallel execution uses the mpirun or mpiexec command. For example: mpirun -np 4 simpleFoam -parallel. During execution, you can monitor load balance and communication volume using tools like top, htop, or dedicated profiling tools (Scalasca, Vampir, etc.).

For parallel calculation results, use the reconstructPar utility to reconstruct the data into a single case. Visualization can be done with ParaView or VisIt. For large-scale data, it's efficient to use parallel I/O or in-situ visualization.

• Load imbalance: Adjust the decomposition method or weights.
• Communication errors: Check MPI library version and network settings.
• Memory shortage: Reduce the number of cells per process or use out-of-core solvers.
• Convergence issues: Review solver settings, relaxation factors, etc.

Use standard benchmark problems (e.g., lid-driven cavity, backward-facing step) to evaluate parallel performance. Key metrics include speedup, efficiency, and strong/weak scaling. Compare with theoretical values (Amdahl's Law, Gustafson's Law) to identify bottlenecks.

• Hybrid parallelization: Combination of MPI and OpenMP.
• GPU acceleration: Using libraries like CUDA, OpenACC.
• Dynamic load balancing
• Fault tolerance: Checkpoint/restart mechanisms.