An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation (Communications in Computational Physics, 2013)
Recently, a new differential discontinuous formulation for conservation lawsnamed 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 beunified under the CPR formulation, which is relatively simple to implement due to itsfinite-difference-like framework. In this paper, a different discontinuous solution spaceincluding both polynomial and Fourier basis functions on each element is employed tocompute broad-band waves. Free-parameters introduced in the Fourier bases are optimized to minimize both dispersion and dissipation errors through a wave propagationanalysis. The optimization procedure is verified with a mesh resolution analysis. Numerical results are presented to demonstrate the performance of the optimized CPRformulation.