A hybrid scheme for the numerical simulation of shock/discontinuity problems

Abstract

To address accuracy issues for direct numerical simulation, a hybrid scheme based on the weighted compact scheme (WCS) and weighted essentially non-oscillatory (WENO) scheme is developed. The new hybrid method incorporates the advantages of both schemes. Time integration is performed using the fourth-order total variation diminishing Runge–Kutta method with a characteristic filter. The accuracy of the scheme is assessed using several benchmark problems. Results show that the proposed scheme produces a more accurate solution for problems involving shocks and discontinuities in comparison with the traditional shock-capturing methods.

Keywords:

• weighted compact scheme
• WENO
• ACM filter
• shock capturing
• non-oscillatory scheme
• double Mach reflection
• shock–vortex interaction
• shock–shear layer interaction
• shock–entropy interaction
• shock tube