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Verification of Euler/Navier–Stokes codes using the method of manufactured solutions
Author(s) -
Roy C. J.,
Nelson C. C.,
Smith T. M.,
Ober C. C.
Publication year - 2004
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.660
Subject(s) - discretization , polygon mesh , euler equations , richardson extrapolation , finite volume method , extrapolation , backward euler method , euler's formula , mathematics , computational fluid dynamics , code (set theory) , numerical analysis , upwind scheme , order of accuracy , computer science , algorithm , mathematical analysis , geometry , numerical stability , physics , set (abstract data type) , mechanics , programming language
Abstract The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes. The Premo code employs a node‐centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second‐order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.