engleski

Parallel block-selective algebraic multigrid in foam-extend

Multigrid methods were originally created for systems of discretised elliptic PDEs but were later expanded and have proven to be efficient for general types of PDEs. Multigrid methods exploit the fact that the point-fixed methods (Jacobi, Gauss-Seidel) tend to quickly reduce the high frequency solution errors, i.e. the errors whose direction corresponds to the largest eigenvalues of the matrix. However, the low frequency errors remain and this is why the performance (convergence) of the fixed-point methods deteriorates. To solve this issue, multigrid methods construct a hierarchy of grids by coarsening the initial grid. The low frequency errors on the finer grid become high frequency errors on the coarser grid and the fixed-point algorithms are able to efficiently reduce these errors. The correction obtained on the coarser grid is then transferred back to the finer grid. Algebraic multigrid methods operate on matrix coefficients directly and do not need a computational grid. We have implemented an algebraic multigrid method in OpenFOAM, an open-source toolbox for Computational Fluid Dynamics based on the Finite Volume Method. The algorithm closely follows the work by K. Stueben and T. Clees and is used to solve the implicitly coupled pressure-velocity system. The numerical discretisation of the linearised equations produces a sparse point-ordered block matrix. To apply the scalar matrix algorithm, a primary matrix is defined and used in the coarsening process. Since the algorithm is used to solve very large systems, a parallel version was developed, without using the subdomain blocking technique as suggested by the original authors. In this work, we present the parallelisation strategy and performance of the block-selective algebraic multigrid for incompressible turbulent flow cases. We will also review the findings on the optimal choice of smoother, multigrid cycle and other settings.

multigrid algorithm, parallel computing, pressure-velocity coupling

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