Evaluation of Optimized CPR Schemes for Computational Aeroacoustics Benchmark Problems

Correction Procedure via Reconstruction (CPR) is a differential discontinuous formulation for conservation laws. In this paper, a recently developed optimized CPR scheme, named frequency optimized CPR (FOCPR), was employed and tested. The idea is to resolve the broadest range of wave frequencies on a given mesh given an acceptable error threshold. In the FOCPR method, both polynomial and Fourier components are included in the basis. The free-parameters of the Fourier basis were chosen to minimize both dispersion and dissipation errors. The performance of the CPR and the FOCPR schemes was compared with a set of CAA problems: the 1D linear wave propagation, the 1D wave propagation on a 2D mesh governed by the 2D Euler equations, the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems: Category 2(C2) and Problem 2 Category 3 (C3P2). It was shown that the FOCPR scheme was able to give more accurate solutions than the CPR scheme for CAA problems on meshes with barely enough resolution for highfrequency waves. For problems with widely varying mesh sizes and non-dimensional wave numbers, the benefit from the FOCPR scheme may be limited.