A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

Abstract

A fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.