A Non-Local Convective Flux Limiter for Upwind-Biased Finite Volume Simulations

Finite volume methods on structured and unstructured meshes often utilize second-order, upwind-biased linear reconstruction schemes to approximate the convective terms, in an attempt to improve accuracy over first-order methods. Limiters are employed to reduce the inherent variable over- and under-shoot of these schemes; however, they also can significantly increase the numerical dissipation of a solution. This paper presents a novel non-local, non-monotonic (NLNM) limiter developed by enforcing cell minima and maxima on dependent variable values projected to cell faces. The minimum and maximum values for a cell are determined primarily through the recursive reference to the minimum and maximum values of its upwind neighbors. The new limiter is implemented using the User Defined Function capability available in the commercial CFD solver Ansys FLUENT. Various simple test cases are presented which exhibit the NLNM limiter’s ability to eliminate non-physical oscillations while maintaining relatively low dissipation of the solution. Results from the new limiter are compared with those from other limited and unlimited second-order upwind (SOU) and first-order upwind (FOU) schemes. For the cases examined in the study, the NLNM limiter was found to improve accuracy without significantly increasing solution convergence rate.