An Adaptive Characteristic-wise Reconstruction WENOZ scheme for Gas Dynamic Euler Equations

TL;DR

The paper introduces AdaWENO, an adaptive scheme that switches between characteristic-wise and component-wise reconstructions to efficiently handle shocks in gas dynamics simulations, maintaining accuracy while reducing computational cost.

Contribution

The novel AdaWENO scheme adaptively combines characteristic-wise and component-wise reconstructions, significantly improving efficiency over traditional methods in shock-capturing simulations.

Findings

AdaWENO maintains non-oscillatory solutions near discontinuities.

AdaWENO is approximately 40% faster than component-wise reconstruction.

Numerical tests validate the effectiveness and efficiency of AdaWENO.

Abstract

Due to its excellent shock-capturing capability and high resolution, the WENO scheme family has been widely used in varieties of compressive flow simulation. However, for problems containing strong shocks and contact discontinuities, such as the Lax shock tube problem, the WENO scheme still produces numerical oscillations. To avoid such numerical oscillations, the characteristic-wise construction method should be applied. Compared to component-wise reconstruction, characteristic-wise reconstruction leads to much more computational cost and thus is not suite for large scale simulation such as direct numeric simulation of turbulence. In this paper, an adaptive characteristic-wise reconstruction WENO scheme, i.e. the AdaWENO scheme, is proposed to improve the computational efficiency of the characteristic-wise reconstruction method. The new scheme performs characteristic-wise reconstruction near discontinuities while switching to component-wise reconstruction for smooth regions. Meanwhile, a new calculation strategy for the WENO smoothness indicators is implemented to reduce over-all computational cost. Several one dimensional and two dimensional numerical tests are performed to validate and evaluate the AdaWENO scheme. Numerical results show that AdaWENO maintains essentially non-oscillatory flow field near discontinuities as the characteristic-wise reconstruction method. Besieds, compared to the component-wise reconstruction, AdaWENO is about 40\% faster which indicates its excellent efficiency.