A fast unsmoothed aggregation algebraic multigrid framework for the large-scale simulation of incompressible flow

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we present an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform sparse matrix-vector multiplications efficiently on all multigrid levels. Our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow. The code is available at http://computationalsciences.org/publications/shao-2022-multigrid.html.