A low dissipative and dispersive scheme with a high order WENO dissipation for unsteady flow analyses

Abstract

General shock-capturing schemes such as TVD, MUSCL, and WENO are robust but time-consuming methods that often give excessively dissipative solutions. On the other hand, although central difference schemes are non-dissipative and are efficient with respect to computing time, they need artificial dissipations for numerical stability and shock- capturing capability. To compensate for the flaws in these two types of schemes, Yee et al. proposed a high-order scheme (hereafter referred to as the "Yee-scheme"), composed of a central flux and a filter obtained from the shock capturing schemes. The Yee-scheme is able to reduce both the numerical dissipation and the computing time for shock-capturing schemes, and the filters play a major role in providing stability and flow feature capturing ability. The main objectives of this work are to investigate the performance of the filters and to propose a new WENO filter, which is derived by splitting the WENO scheme into a weighted central flux part and a numerical dissipation part. Through several un-steady flow analyses such as a convecting vortex, shock/turbulence interaction, and mixing layer/shock interaction, we show the characteristics of the filters and validate the proposed WENO filter by proving that it can be used as an efficient filter for unsteady calculations.