RKDG methods with WENO limiters for unsteady cavitating flow

Abstract

In this paper, we develop the Runge–Kutta discontinuous Galerkin (RKDG) methods with the finite volume weighted essentially non-oscillatory (WENO) reconstruction as limiters to solve for the unsteady cavitating flow under the employment of the isentropic one-fluid model. To treat the cavitating flow and suppress the possible spurious oscillations in the vicinity of the cavitation boundary, the TVB limiter is used as an indicator to detect the “troubled cells” and hence take the advantage of utilizing the WENO reconstruction for the freedoms of the RKDG methods. Numerical results are provided to illustrate the viability of these procedures.