Discontinuous Solutions Using the Method of Manufactured Solutions on Finite Volume Solvers

When applying the method of manufactured solutions on computational fluid dynamic software, it is a requirement that all solutions be continuous on the computational domain. This stipulation is limiting for the verification and validation of numerical solutions where discontinuities are frequent. In...

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Bibliographic Details
Published in:AIAA journal 2015-08, Vol.53 (8), p.2369-2378
Main Authors: Grier, Benjamin, Figliola, Richard, Alyanak, Edward, Camberos, José
Format: Article
Language:English
Subjects:
Aerodynamics
Aircraft
Computational fluid dynamics
Constraining
Discontinuity
Exact solutions
Least squares method
Mathematical analysis
Mathematical models
Solvers
Structured grids (mathematics)
Transformations
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Summary:When applying the method of manufactured solutions on computational fluid dynamic software, it is a requirement that all solutions be continuous on the computational domain. This stipulation is limiting for the verification and validation of numerical solutions where discontinuities are frequent. In an effort to adapt the standard method of manufactured solutions procedure, we propose a piecewise approach for modeling solutions with discontinuities. Linearly and quadratically exact transformations are used for determining the exact solutions and source terms for cells split by discontinuities. Upwind manufactured solutions are initialized and a least squares fit is used to solve for solutions downwind of the discontinuity such that the Rankine–Hugoniot conditions are satisfied. The codes used throughout this research are finite volume, 1st and 2nd order, inviscid schemes combined with uniform structured grids. This study shows that a modified method of manufactured solutions procedure can be performed with fully general discontinuous solutions yielding 1st order convergences typically associated with shocks.
ISSN:0001-1452
1533-385X
DOI:10.2514/1.J053725