Numerical simulation of upwinding schemes applied to complex fluid dynamics equations

Abstract

In this work, the nonlinear Euler equations of gas dynamics are employed for a comparative study of the frequently used flux limiters, namely: the consecrated ARORA-ROE, van Albada, CUBISTA and ADBQUICKEST; and two rational functions TVD-CBC-based TOPUS and SDPUS-C1 schemes. The comparison is mainly done in terms of their abilities in resolving discontinuities, reproducing complex flow phenomena and accuracy. It is concluded that both TOPUS and SDPUS-C1 can be considered as alternative tools for computer simulations of fluid flow. As application, the corresponding SDPUS-C1 scheme is employed to simulate 2D/3D incompressible flows with moving free surfaces.