An Improved High-order Adaptive Mesh Refinement Framework for Shock-turbulence Interaction Problems based on cell-centered finite difference schemes

TL;DR

This paper introduces a high-order adaptive mesh refinement framework with a staggered-grid arrangement and hybrid interpolation strategies, improving the robustness and accuracy of shock-turbulence interaction simulations.

Contribution

It develops a novel hybrid interpolation method combining non-conservative WENO and conservative schemes for stable shock capturing on staggered grids.

Findings

Accurately resolves complex shock-turbulence interactions.

Mitigates numerical instabilities at shocks.

Demonstrates robustness on canonical tests.

Abstract

This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers instead of at the vertices, is presented to address the boundary conservation issues encountered in previous studies. The key ingredient in the AMR framework, i.e., the high-order nonlinear interpolation method applied in the prolongation step together with the determination of fine-grid boundary conditions, are re-derived for staggered grids following the procedures in prior work [1] and are thus used here. Meanwhile, a high-order restriction method is developed in the present study as the coarse and fine grid solutions are non-collocated in this configuration. To avoid non-conservative interpolation at discontinuous cells that could incur instabilities, a hybrid interpolation strategy is proposed in this work for the first time, where the non-conservative WENO interpolation is applied in smooth regions whereas the second-order conservative interpolation is applied at shocks. This significantly mitigates the numerical instabilities introduced by non-conservative interpolation and pointwise replacement. The two interpolation approaches are seamlessly coupled through a troubled-cell detector achieved by a scale-irrelevant Riemann solver in a robust way. The present work is developed on a publicly available block-structured adaptive mesh refinement framework AMReX [2]. The canonical tests demonstrate that the proposed method is capable of accurately resolving a wide range of complex shock-turbulence interaction problems that have been proven intricate for existing approaches