An Efficient Low-Dissipation High-Order TENO Scheme for MHD Flows

Abstract

In this paper, an efficient low-dissipation high-order TENO scheme is proposed for ideal MHD flows. For high computational efficiency, a troubled-cell indicator based on the ENO-like stencil selection strategy in TENO schemes is introduced to isolate the discontinuities from smooth regions. While the high-order linear scheme is adopted for the smooth regions, a low-dissipation TENO scheme is applied for capturing discontinuities detected by the troubled-cell indicator. The case-independent parameters are given based on spectral analysis. Both the governing equations of the ideal MHD and the Hamilton–Jacobi type constrained transport equation for divergence-free condition can be solved by the newly proposed scheme. Since most computational regions are resolved by the linear scheme without expensive characteristic decomposition, flux splitting and nonlinear weight calculation, the proposed scheme is highly efficient. A set of benchmark cases has been simulated to demonstrate the performance of the proposed scheme. Numerical results reveal that remarkable speedup is achieved by the present scheme while the oscillation-free property and the high-order accuracy are preserved.