A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws

Abstract

With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. The local flow structures are classified as smooth or nonsmooth scales, and the hybrid numerical discretization scheme is applied correspondingly, i.e. the high-order upwind linear scheme without characteristic decomposition is employed for resolving smooth scales while the nonlinear low-dissipation TENO scheme is adopted to capture discontinuities. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter C_T. In contrast to the thresholds of other discontinuity indicators, which are typically defined in physical space, C_T takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks.