All Equalities Are Equal, but Some Are More Equal Than Others: The Effect of Implementation Aliasing on the Numerical Solution to Conservation Equations
Will Trojak, Ash Scillitoe, Rob Watson
TL;DR
This paper examines how aliasing affects the numerical solution of conservation equations, highlighting that storing conserved variables reduces dissipation and that gradient calculation methods have minimal impact, with implications for high-order simulations.
Contribution
It provides a detailed analysis of aliasing effects on conservation equations, comparing storage strategies, gradient methods, and precision impacts in high-order numerical schemes.
Findings
Storing conserved variables introduces less dissipation.
Aliasing effects grow factorially with the order of the method.
Gradient calculation differences are generally small, favoring the product rule.
Abstract
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.…
Click any figure to enlarge with its caption.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
Figure 27
Figure 28
Figure 29
Figure 30Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsFluid Dynamics and Turbulent Flows · Computational Fluid Dynamics and Aerodynamics · Model Reduction and Neural Networks