A scalable geometric multigrid solver for nonsymmetric elliptic systems with application to variable-density flows

摘要

Highlights?The independence of the convergence rate from the size of the system is shown for uniform and nonuniform grids.?Our method is robust to large and sharp density variations and can be applied to two-phase flow problems.?Strong and weak scaling results show scalability of our implementation up to tens of thousands of processors.AbstractA geometric multigrid algorithm is introduced for solving nonsymmetric linear systems resulting from the discretization of the variable density Navier–Stokes equations on nonuniform structured rectilinear grids and high-Reynolds number flows. The restriction operation is defined such that the resulting system on the coarser grids is symmetric, thereby allowing for the use of efficient smoother algorithms. To achieve an optimal rate of convergence, the sequence of interpolation and restriction operations are determined through a dynamic procedure. A parallel partitioning strategy is introduced to minimize communication while maintaining the load balance between all processors. To test the