The present works deal with the performance of higher-order CFD methods in compressible flows with shock waves. We solve the shock wave-strong vortex interaction problem with the discontinuous Galerkin (DG) method, and the performance of the numerical schemes is analyzed in qualitative and quantitative manners. We model the shock wave-vortex interaction phenomenon as a two-dimensional inviscid flow problem. Due to the interaction of the shock wave and vortex, physical phenomena such as complex shock structure, vortex structure, and evolution of acoustic waves occur. We observe and analyze these flow physics with the unsteady numerical results, and establish the criteria to compare the results of the higher-order methods. As shock capturing methods, hierarchical multi-dimensional limiting process (hMLP) and hMLP with the troubled-boundary detector (hMLP_BD) are used with the DG method. The DG method with hMLP and hMLP_BD are applied to solve the problem in meshes of various types and sizes. Then, the numerical schemes are compared and analyzed by verifying capability to describe complex flow physics and evaluating unsteady flow solutions. In order to identify the causes of the order-of-accuracy degradation of higher-order methods in the shock wave-strong vortex problem, additional problems are set up and tested. Through these additional tests, we can examine the effect of each factor on order-of-accuracy degradation. As a result, projection error and shock-driven oscillations are the main causes of order-of-accuracy degradation in higher-order methods.
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A Study on the Performance of Higher-Order Methods through Shock Wave-Strong Vortex Interaction Problem
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