A low-dissipation finite-volume method based on a new TENO shock-capturing scheme

摘要

In Fu et al. (2016), a family of high-order TENO shock-capturing schemes has been proposed for compressible fluid simulations within a finite-difference framework. With the TENO weighting strategy, each candidate stencil is either applied for the final reconstruction with its optimal weight or discarded completely when crossed by discontinuities. In this paper, with the observation that the local flow scales can be judged to be smooth or non-smooth explicitly, we propose a novel low-dissipation finite volume method based on a new TENO reconstruction. Firstly, a new ENO-like stencil selection paradigm, which adapts between three three-point small stencils and a large candidate stencil, is proposed. The resulting TENO scheme inherits the low-dissipation advantage of original TENO schemes and can be extended to arbitrarily high-order reconstruction without significant complexity increase. The optimal background linear scheme on the three small stencils and that on the large stencil can be optimized either approaching high-order accuracy or better spectral properties separately. Secondly, within the finite volume framework, a "low-dissipation" Riemann solver is applied for flux computing when the large candidate stencils for both the left-and right-side reconstruction are judged as smooth whereas a robust "dissipative" Riemann solver is adopted when one large candidate stencil crosses discontinuities. Since the numerical dissipation from both the reconstruction stage and the flux computing stage can be tuned according to the TENO weighting strategy, the proposed finite-volume method is less-dissipative and provides additional flexibility to handle challenging simulations. A set of benchmark cases is simulated to assess the performance of proposed method. (C) 2018 Elsevier B.V. All rights reserved.