engleski

Selective algebraic multigrid for implicitly coupled pressure-velocity system

Systems of equations are dominated by inter- equation coupling terms. The conventional methods solve the system in a sequential manner, solving each equation separately and explicit treatment of coupled variables. Modern High-Performance Computing clusters with substantial memory resources have enabled development of coupled algorithms which rely on linearisation of cross coupling terms and solving the system in an implicit manner. This study presents a selective algebraic multigrid for the implicitly coupled pressure- velocity system in the framework of Finite Volume Method. The solution of this system is a saddle point. To remedy the problem, the pressure equation is derived as a Schur complement. The resulting system is point-ordered. Single-unknown interpolation has been used, i.e. the interpolation formula is calculated from the pressure equation, excluding the cross-couplings from the momentum equation. Thus, interpolation formula is the same for all unknowns corresponding to a single point. Benefits of the implicit coupling of the pressure and velocity equations are shown and compared to the conventional segregated algorithm. Performance of the selective algebraic multigrid is compared to the aggregation-based algebraic multigrid.

algebraic multigrid ; implicit coupling ; pressure-velocity coupling ; foam-extend

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