An Efficient Hybrid Weno Scheme with a Novel Scale Separation Criterion

The WENO family schemes have been widely used in various compressible turbulence flow simulations due to its excellent shock-capturing capability and high resolution. However, due to the massive calculation is needed by WENO scheme, the variable-based flux is usually used in engineering numerical calculation, rather than characteristic-based reconstruction that require matrix operation. For problems containing strong shocks, variable-based reconstruction may produces numerical oscillations, while characteristic-based reconstruction rarely do. In this paper, a novel scale separation mechanism without free parameter is proposed to construct an efficient hybrid WENO scheme, i.e. WENO-H, by which the characteristic-based or variable-based reconstruction can be accurately selected for different region of the flow, so as to obtain a higher resolution and more stable shock capturing scheme while improving the efficiency. According to the novel scale separation mechanism the new scheme performs characteristic-based reconstruction near discontinuities and switches to variable-based reconstruction for smooth region. Linear variable-based fluxes with less computation are used directly in the smooth region, while nonlinear WENO-Z and more robust characteristic-base fluxes are used in the discontinuous region. Several one dimensional and two dimensional numerical tests are performed to validate and evaluate the scheme. Numerical results shows that WENO-H series schemes maintain essentially non-oscillatory flow filed near discontinuities. Besides, compared to the WENO-Z, the WENO-H series schemes are 10% faster in 1D problem and 30% faster in 2D problem, and saved more than 1.6 times computational cost compared with TENO.