Improvement of Mixing Function for Modified Upwinding Compact Scheme

TL;DR

This paper introduces a modified upwinding compact scheme that effectively captures shocks sharply while maintaining high order accuracy and resolution in smooth regions, improving turbulence and shock interaction simulations.

Contribution

It develops a new control function and shock detector for the MUCS, enhancing shock capturing without sacrificing accuracy in smooth areas.

Findings

Successfully captures shocks sharply in 2-D Euler simulations

Maintains high order accuracy and resolution in smooth regions

Improves shock boundary layer and shock acoustic interaction modeling

Abstract

The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified upwinding compact scheme which uses an effective shock detector to block compact scheme to cross the shock and a control function to mix the flux with WENO scheme near the shock. The new scheme makes the original compact scheme able to capture the shock sharply and, more important, keep high order accuracy and high resolution in the smooth area, which is particularly important for shock boundary layer and shock acoustic interactions. This work is a continuation to modify the control function for the modified up-winding compact scheme (MUCS). Numerical results show the scheme is successful for 2-D Euler.