Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics

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• 作者：Dinshaw S. Balsara
• 关键词：Positivity ; Higher order Godunov schemes ; Reconstruction ; ADER ; WENO ; Hydrodynamics ; Magnetohydrodynamics
• 刊名：Journal of Computational Physics
• 出版年：2012
• 出版时间：15 September, 2012
• 年：2012
• 卷：231
• 期：22
• 页码：7504-7517
• 全文大小：1133 K

文摘

The method presented here does not degrade the order of accuracy for smooth flows. Via a stringent test suite, we document that our method works well on structured meshes for all orders of accuracy up to four. When the same test problems are run without the positivity preserving methods, one sees a very clear degradation in the results, highlighting the value of the present method. The results are compelling because realistic simulation of several difficult astrophysical and space physics problems requires the use of parameters that are similar to the ones in our test problems.

In this work, weighted non-oscillatory reconstruction was applied to the conserved variables, i.e. we did not apply the reconstruction to the characteristic variables, which would have made the scheme more expensive. Yet, used in conjunction with the positivity preserving schemes presented here, the less expensive reconstruction works very well in two and three dimensions. This suggests that when designing robust, high accuracy schemes, having a self-adjusting positivity criterion is almost as important as the non-linear hybridization.