Astronomy and Astrophysics – Astrophysics
Scientific paper
1993-11-06
Astronomy and Astrophysics
Astrophysics
29 pages + 21 figures (compressed, uuencoded PostScript, appended), LaTeX 2.09 (AAS preprint substyle v3.0)
Scientific paper
We investigate asymptotic convergence in the~$\Delta x \!\rightarrow\! 0$ limit as a tool for determining whether numerical computations involving shocks are accurate. We use one-dimensional operator-split finite-difference schemes for hydrodynamics with a von Neumann artificial viscosity. An internal-energy scheme converges to demonstrably wrong solutions. We associate this failure with the presence of discontinuities in the limiting solution. Our extension of the Lax-Wendroff theorem guarantees that certain conservative, operator-split schemes converge to the correct continuum solution. For such a total-energy scheme applied to the formation of a single shock, convergence of a Cauchy error approaches the expected rate slowly. We relate this slowness to the effect of varying diffusion, due to varying linear artificial-viscous length, on small-amplitude waves. In an appendix we discuss the scaling of shock-transition regions with viscous lengths, and exhibit several difficulties for attempts to make extrapolations.
Chernoff David F.
Kimoto Paul A.
No associations
LandOfFree
Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence properties of finite-difference hydrodynamics schemes in the presence of shocks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-258464