A Novel High-Resolution TENO Scheme with Adaptive Artificial Anti-Diffusion

Abstract

Low-dissipation higher-order approaches are crucial for flows characterized by shocks and turbulence. The broad applicability of conventional WENO/TENO systems for accurately capturing shocks makes them a preferred option for simulating complex flow phenomena. Nonetheless, the inherent numerical diffusion in these techniques poses a significant challenge in simulating multiscale turbulent flow. This study mitigates the inherent numerical damping by using locally adaptive higher-order artificial anti-diffusion. A switching function quantifies the extent of anti-dissipation in the smooth zone and assesses the local variation of flow field variables. To assure stability, the anti-diffusion coefficient is meticulously assessed using two fixed free parameters. Next strategy utilizes a fourth-order central difference scheme in the highly smooth region, incorporating an additional coefficient modified in a binary fashion. The adaptive regulating parameter $C_T$ in the fifth-order TENO scheme is integrated with the anti-diffusive function. It is recognized that the new scheme exhibits less numerical diffusion than the original TENO scheme. This is also reflected in the numerical experiments, encompassing a series of benchmark test scenarios featuring shock and fine-scale structures. It is shown that the proposed scheme could resolve the turbulent scales with much higher resolution and capture the shock sharply. It is worth noting that these strategies can easily be implemented in the other variations of the TENO scheme.