engleski

IMPLICITLY COUPLED PRESSURE–VELOCITY SOLVER WITH SELECTION ALGEBRAIC MULTIGRID

In the past decade, the attention of computational fluid dynamics (CFD) community has been focused on developing coupling methods for the pressure- velocity system. The traditional, widely used solution techniques were developed to accomodate the limited capabilities of contemporary computers, and rely on decoupling the equations and solving them in separate linear systems, treating the other variable explicitly. Implicitly coupled technique retains the linear coupling of pressure and velocity by solving them in a single linear system, and employs a Poisson pressure equation to counteract the zero terms on the diagonal of the matrix. We have implemented the implicitly coupled solver into OpenFOAM, an open source CFD toolbox. Since the pressure equation represents the most challenging part of the solution, we employ a selection algebraic multigrid method, which is an efficient linear solver for discrete elliptic equations, in synergy with the incomplete lower–upper factorisation, based on Crout’s algorithm (ILUC) as a smoother. The construction of coarse level matrices in selection algebraic multigrid relies on selecting the representative equations from the fine level matrix, based on the strength of connection criterion, and calculating the coarse operator based on Galerkin’s variational principle. Since the coarsening process is entirely sequential, we present a stategy for parallelisation of the multigrid method and the outcome in terms of operator complexity and convergence rate for cases with complex flow features.

multigrid algorithm, parallel computing, pressure-velocity coupling

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