An improved flux vector splitting method for characteristic-wise WENO schemes of the Euler equations

Abstract

Steger-Warming (SW) [1] and Lax-Friedrich-type (LF) [2] flux vector splitting methods are used extensively by shock capturing WENO schemes in varieties of compressible flow simulations. Due to the less dissipation, the SW method is preferred in flow calculations that require fine scale structures such as direct numerical simulation of turbulence. However, this paper shows that, even if the characteristic-wise WENO scheme is used, the SW method may still exhibit some oscillations near contact discontinuities, while the LF method does not. Analysis similar to the reference [3] shows that, using the SW method may make the characteristic-wise WENO scheme become close the component-wise WENO scheme near subsonic contact discontinuities. Based on that, an improved flux vector splitting method, which adjusts the eigenvalues of the flux vector splitting in the characteristic-wise WENO procedure, is proposed to obtain the low-dissipation property and prevent contact discontinuity oscillations at the same time. Numerical experiments are performed to validate and evaluate the new method. Numerical results show that the proposed method keeps the non-oscillatory flow field near discontinuities as LF method and also avoids smearing out other flow regions, similar to the SW method.

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