Comparison of Errors Caused by Flux Limiters on the Numerical Solution of Advection-Diffusion Problem

Abstract

Flux limiters are widely used in numerical simulations to prevent spurious oscillation in the flow with strong property gradients. However, applying flux limiter on flow without strong property gradient such as advection-diffusion flow can cause errors. This article discusses the errors caused by several flux limiters in advection-diffusion flow solution. A method for applying one-dimensional limiters to two-dimensional unstructured mesh was also suggested. The error was measured by comparing the finite volume solution of a test case with a reference solution. The study shows that the calculation error of second-order finite volume with flux limiter was higher than that of second-order finite volume without limiter. However, the error of third-order finite volume with flux limiter is less than that of second-order without flux limiter. Among the flux limiters tested in this study, Venkatakrishnan’s flux limiter produces the highest error, followed by Van leer’s limiter, EULER and SMART limiter.