Commun. Comput. Phys., 13 (2013), pp. 1265-1291.


An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation

Yi Li 1*, Z. J. Wang 1

1 Department of Aerospace Engineering and CFD Center, Iowa State University, Ames, IA 50011, USA.

Received 30 July 2011; Accepted (in revised version) 7 May 2012
Available online 8 October 2012
doi:10.4208/cicp.300711.070512a

Abstract

Recently, a new differential discontinuous formulation for conservation laws named the Correction Procedure via Reconstruction (CPR) is developed, which is inspired by several other discontinuous methods such as the discontinuous Galerkin (DG), the spectral volume (SV)/spectral difference (SD) methods. All of them can be unified under the CPR formulation, which is relatively simple to implement due to its finite-difference-like framework. In this paper, a different discontinuous solution space including both polynomial and Fourier basis functions on each element is employed to compute broad-band waves. Free-parameters introduced in the Fourier bases are optimized to minimize both dispersion and dissipation errors through a wave propagation analysis. The optimization procedure is verified with a mesh resolution analysis. Numerical results are presented to demonstrate the performance of the optimized CPR formulation.

AMS subject classifications: 76

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Key words: CPR (correction procedure via reconstruction), hybrid discontinuous space, wave propagation analysis, unstructured meshes.

*Corresponding author.
Email: yili@iastate.edu (Y. Li), zjw@iastate.edu (Z. J. Wang)
 

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