An Efficient Hybrid Compact-WENO Scheme for Computational Aerodynamics

Abstract

The hybrid compact-WENO scheme is an effective method to construct a high-resolution shock-capturing scheme for computational aerodynamics. Ren et al. (J. Comput. Phys. 192:365-386, 2003) presented a characteristic-wise hybrid compact-WENO scheme, which combines the high-resolution property of the compact scheme with the shock-capture ability of the WENO scheme. However, it needs to deal with the block-tridiagonal system of linear equations when applied to solve systems of hyperbolic conservation laws (such as Euler equations). Therefore, the scheme is computationally expensive, which limits its application in engineering practice. In this paper, we present a new hybrid compact-WENO scheme. This new scheme also uses the characteristic-wise method. However, it avoids solving the block-tridiagonal system of linear equations by cleverly utilizing the monotone-preserving limiter and the higher dissipative Lax-Friedrich flux splitting. As a result, the scheme has a much higher efficiency than Ren’s scheme. A series of numerical experiments verify the high-resolution property, excellent shock-capture ability, and high efficiency of the presented scheme. Therefore, it is suitable for engineering applications.