All Equalities Are Equal, but Some Are More Equal Than Others: The Effect of Implementation Aliasing on the Numerical Solution to Conservation Equations
We investigate the effect of aliasing when applied to the storage of variables, and their reconstruction for the solution of conservation equations. In particular, we investigate the effect on the error of storing primitives versus conserved variables for the Navier-Stokes equations. It was found th...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
25.01.2019
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Subjects | |
Online Access | Get full text |
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Summary: | We investigate the effect of aliasing when applied to the storage of
variables, and their reconstruction for the solution of conservation equations.
In particular, we investigate the effect on the error of storing primitives
versus conserved variables for the Navier-Stokes equations. It was found that
storing the conserved variables introduces less dissipation and that the
dissipation caused by constructing the conversed variable from the primitives
grows factorially with the order. Hence, this problem becomes increasingly
important with the continuing move towards higher orders. Furthermore, the
method of gradient calculation is investigated, as applied to the viscous
fluxes in the Navier-Stokes equations. It was found that in most cases the
difference was small, and that the product rule applied to the gradients of the
conserved variables should be used due to a lower operation count. Finally,
working precision is investigated and found to have a minimal impact on
free-stream-turbulence-like flows when the compressible equations are solved,
except at low Mach numbers. |
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DOI: | 10.48550/arxiv.1901.08884 |