Assessment of Errors Caused by Several Flux Limiters in Advection-Diffusion Flow Solution

This article discusses the errors caused by several flux limiters in advection-diffusion flow solutions. Numerous affordances have been developed to reduce the spurious oscillation during the last decade to solve various problems arising in mathematical physics. Flux limiters are widely used in numerical simulations to prevent spurious oscillation in the flow with strong property gradients. However, applying a flux limiter on flow without a strong property gradient such as advection-diffusion flow can cause errors due to the action of the limiter on the higher-order part of the flux. A method for applying one-dimensional limiters to two-dimensional unstructured mesh was also suggested. By contrasting a test case's finite volume solution with a reference solution, the error was calculated. According to the study, second-order finite volumes with flow limiters had greater calculation errors than those without limiters.

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.