A novel high-order low-dissipation TENO-THINC scheme for hyperbolic conservation laws

Abstract

The high-order low-dissipation shock-capturing scheme is important for compressible fluid simulations, in particular for cases where both shock and turbulence present. However, the competing requirements for resolving the small-scale turbulence structures with low dissipation and capturing the discontinuities sharply render it non-trivial for numerical development. In this work, based on a novel parameter-free discontinuity-detection criterion, a new shock-capturing framework is proposed by combining the standard TENO (targeted essentially non-oscillatory) scheme for smooth regions with the non-polynomial based THINC (tangent of hyperbola for INterface capturing) reconstruction for non-smooth discontinuities. The resulting hybrid scheme retains the low-dissipation property of TENO scheme for smooth flow scales and the discontinuity-resolving capability of THINC reconstruction for shock and contact waves. A set of benchmark simulations involving a wide range of length scales demonstrates that the new TENO-THINC scheme performs significantly better than the standard TENO scheme without the necessity of parameter tuning case by case, and thus is promising for more complex compressible flow predictions where the excessive numerical dissipation of existing schemes prevents the targeted flow structures from being properly resolved. Moreover, the present results serve as the state-of-the-art references for future numerical method development.