Volume 13, Issue 5
An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation

Yi Li & Z. J. Wang

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

Published online: 2013-05

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  • 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.

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@Article{CiCP-13-1265, author = {}, title = {An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {5}, pages = {1265--1291}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.300711.070512a}, url = {http://global-sci.org/intro/article_detail/cicp/7274.html} }
TY - JOUR T1 - An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation JO - Communications in Computational Physics VL - 5 SP - 1265 EP - 1291 PY - 2013 DA - 2013/05 SN - 13 DO - http://doi.org/10.4208/cicp.300711.070512a UR - https://global-sci.org/intro/article_detail/cicp/7274.html KW - AB -

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.

Yi Li & Z. J. Wang. (2020). An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation. Communications in Computational Physics. 13 (5). 1265-1291. doi:10.4208/cicp.300711.070512a
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