Block-selective algebraic multigrid for implicitly coupled pressure-velocity system

To remedy the problem, we have implemented a Block-Selective Algebraic Multigrid in foam-extend which is a community driven fork of OpenFOAM, an open-source CFD software library for arbitrary polyhedral Finite Volume Method. Coarsening is done by selecting a set of equations which will be solved on the coarse level, based on a heuristic algorithm. Prolongation operator is calculated from the approximation of the algebraically smooth error. Restriction and coarse level matrix are formed based on a variational principle for a symmetric positive-definite matrix. To apply the algorithm on the matrix arising from the discretisation of the implicitly coupled pressure-velocity system, a primary matrix must be chosen by calculating a norm of the block-coefficient.