Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient: Gradient Limiters for High-Reynolds-Number Flows

Abstract

This article aims at seeking feasible gradient limiter functions for our newly developed high-resolution numerical method for incompressible Navier-Stokes equations. Because the solution gradients are solved directly with their governing equations, the implementation of limiter functions becomes an easy task. Several limiter functions are proposed to inhibit the occurrence of local extrema at computational cell boundaries. Numerical tests on pure convection as well as practical flow problems are conducted to evaluate their benefits. A mixed limiter function via simple hybridization is then devised and incorporated to yield accurate results by getting rid of impractical oscillatory distributions. In this manner, simulations of high-Reynolds-number flow problems can be put into practice with affordable computational cost.