A Next-Generation DBNS Solver: Accurate Solutions and Fast Multigrid Driven Convergence

摘要

Accurate density-based finite-volume numerical discretizations for all-speeds, with very efficient implicit solution methods on unstructured grids, are proposed. Two best-in-class flux-difference splitting (Roe) and flux-vector splitting(AUSM+) numerical flux discretizations are used, together with a least-squares linear reconstruction that guarantes second order accuracy. A highly-efficient solution method is proposed, that combines three key ingredients in a nested manner: geometric multigrid, a low-storage Runge Kutta multistage algorithm, and a combination of point-coupled and full-coupled smoothing steps. This method allows converged solutions to be obtained in as few as 5-10 multigrid cycles for practically all speed regimes, on unstructured grids.