O artigo é de autoria de Nicholas D. P. Silva, Carlos H. Marchi, Luciano K. Araki, Rafael B. R. Borges, Guilherme Bertoldo e Chi-Wang Shu.
Abstract
Richardson extrapolation is a powerful approach for reducing the spatial discretization errors and increasing, in this way, the accuracy of the computed solution obtained by use of many numerical methods for solving different scienti c and engineering problems. This approach has been used in a variety of computational fuid dynamics problems to reduce the numerical errors, but its use has been restricted mainly to the computation of incompressible fuid fows and on grids with coincident nodes. In this work we present a completed repeated Richardson extrapolation (CRRE) procedure for a more
generic type of grid not necessarily with coincident nodes, and test it on compressible fuid fows. Three tests are performed for one-dimensional and quasi-one-dimensional Euler equations: (i) Rayleigh fow, (ii) isentropic flow, and (iii) adiabatic fow through a nozzle. The last test involves a normal shock wave. To build a simple solver, these problems are solved by a fi rst-order upwind-type fi nite difference method as the base scheme. The normal shock wave problem is also solved with a high-order weighted essentially nonoscillatory (WENO) scheme to compare it with the CRRE procedure. The procedure we propose can increase the achieved accuracy and signi cantly decrease the magnitude of the spatial error in all three tests. Its performance is best demonstrated in the Rayleigh fow test, where the spatial discretization error is reduced by seven orders of magnitude and the achieved accuracy is increased from 0.998 to 6.62 on a grid with 10,240 nodes. Similar performance is observed for isentropic fow, for which the spatial discretization error is reduced by nine orders of magnitude and the achieved accuracy is increased from 0.996 to 6.73 on a grid with 10,240 nodes. Finally, in adiabatic fow with a normal shock wave, the procedure can reduce the spatial discretization error both upstream and downstream of the shock. However, the more expensive high-order WENO scheme results in errors of lower magnitude upstream of the shock and a sharper shock transition for this shocked test case.
generic type of grid not necessarily with coincident nodes, and test it on compressible fuid fows. Three tests are performed for one-dimensional and quasi-one-dimensional Euler equations: (i) Rayleigh fow, (ii) isentropic flow, and (iii) adiabatic fow through a nozzle. The last test involves a normal shock wave. To build a simple solver, these problems are solved by a fi rst-order upwind-type fi nite difference method as the base scheme. The normal shock wave problem is also solved with a high-order weighted essentially nonoscillatory (WENO) scheme to compare it with the CRRE procedure. The procedure we propose can increase the achieved accuracy and signi cantly decrease the magnitude of the spatial error in all three tests. Its performance is best demonstrated in the Rayleigh fow test, where the spatial discretization error is reduced by seven orders of magnitude and the achieved accuracy is increased from 0.998 to 6.62 on a grid with 10,240 nodes. Similar performance is observed for isentropic fow, for which the spatial discretization error is reduced by nine orders of magnitude and the achieved accuracy is increased from 0.996 to 6.73 on a grid with 10,240 nodes. Finally, in adiabatic fow with a normal shock wave, the procedure can reduce the spatial discretization error both upstream and downstream of the shock. However, the more expensive high-order WENO scheme results in errors of lower magnitude upstream of the shock and a sharper shock transition for this shocked test case.
Este artigo é uma produção do Grupo de Pesquisa em CFD, propulsão e aerodinâmica de foguetes da UFPR (http://www.cfd.ufpr.br/), em colaboração com os professores Borges, Bertoldo e Shu de outras instituições, e resultado da tese de doutorado de Nicholas D. P. Silva.
O artigo está disponível em https://doi.org/10.1016/j.apm.2019.07.024
Um arquivo PDF do artigo completo pode ser solicitado através do
e-mail chmcfd@gmail.com
O artigo está disponível em https://doi.org/10.1016/j.apm.2019.07.024
Um arquivo PDF do artigo completo pode ser solicitado através do
e-mail chmcfd@gmail.com
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