Very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control

TL;DR

This paper introduces a new family of very-high-order TENO schemes with adaptive accuracy and dissipation control, improving robustness and performance in simulating highly compressible flows across a wide Mach number range.

Contribution

The paper proposes a unified framework for constructing arbitrarily high-order TENO schemes with adaptive accuracy and dissipation, enhancing their applicability to complex flow simulations.

Findings

Excellent performance in predicting highly compressible flows.

Good robustness for conventional gas dynamics.

Preserves ENO-property with positivity-preserving flux limiter.

Abstract

In this paper, a new family of very-high-order TENO schemes with adaptive accuracy order and adaptive dissipation control (TENO-AA) is proposed. The new framework allows for constructing arbitrarily high-order TENO schemes in a unified paradigm and the yielded nonlinear schemes gradually reduce to low-order reconstructions by judging the smoothness with the ENO-like stencil selection strategy. In order to control the nonlinear numerical dissipation adaptively, the flow scales are first measured by examining the first-order undivided difference and the cut-off constant $C_T$ in the TENO weighting strategy is adapted based on the corresponding measurement. With one set of optimal parameters, the newly proposed TENO schemes are designed to deliver excellent performance for predicting highly compressible flows with a wide range of Mach numbers. While the new very-high-order TENO schemes feature good robustness for conventional gas dynamics, the ENO-property is well preserved with the assistant of a positivity-preserving flux limiter for extreme simulations. Without loss of generality, the typical eight- and ten-point TENO-AA schemes are constructed. A set of benchmark simulations are computed to demonstrate the performance of the proposed TENO schemes.