engleski

Parallelisation of selective algebraic multigrid for block–pressure– velocity system in OpenFOAM

In the world of computational fluid dynamics (CFD), solving the governing equations of incompressible, turbulent, single-phase fluid flow still represents the basis of many industrial and academic applications. The implicitly coupled (monolithic) solution approach is still being developed and investigated for industrial- size applications. A parallel selection algebraic multigrid algorithm (AMG) based on the domain decomposition method is presented, applied for the solution of the linearised implicitly coupled pressure–velocity system discretised by the finite volume method, implemented in OpenFOAM. Since the setup phase of the selection AMG, i.e.sorting the equations into coarse and fine subsets is inherently sequential, it was decided to perform the setup phase locally on each processing unit. The prolongation matrix for transferring the correction from coarse to fine level and restriction matrix for transferring the residual from fine to coarse level are assembled locally as well. Parallel communication is necessary only for the calculation of the coarse level matrix, i.e.the matrix elements which describe the cross- coupling of equations located on different processing units. A localised version of the ILU factorisation based on Crout’s algorithm is used as a smoother in the multigrid cycle. A detailed analysis of the coarse level matrix complexity is conducted in the context of the finite volume method in domain decomposition mode. The performance and scaling of our parallel implementation is investigated for two test cases and the possible drawbacks of the method are given.

Selection algebraic multigrid ; Multigrid parallelisation ; Pressure–velocity

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