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On the Accuracy of Bicompact Schemes as Applied to Computation of Unsteady Shock Waves
Computational Mathematics and Mathematical Physics ( IF 0.7 ) Pub Date : 2020-06-30 , DOI: 10.1134/s0965542520050061
M. D. Bragin , B. V. Rogov

Abstract

Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system. It is shown that a nonmonotone bicompact scheme has a higher order of convergence in domains of influence of unsteady shock waves. If spurious oscillations are suppressed by applying a conservative limiting procedure, then the bicompact scheme, though being high-order accurate on smooth solutions, has a reduced (first) order of convergence in the domains of influence of shock waves.



中文翻译:

双紧凑方案在非定常冲击波计算中的精度研究

摘要

考虑在空间上具有古典近似四阶且在时间上具有更高阶(至少第二阶)的双紧凑方案。研究了它们的精度,并将其应用于拟线性双曲守恒律系统,该系统具有不连续解,涉及具有可变传播速度的冲击波。浅水方程式被用作这种系统的一个例子。结果表明,非单调双紧方案在非稳定冲击波的影响域中具有较高的收敛阶。如果通过应用保守的限制程序来抑制杂散振荡,则双紧凑方案尽管在光滑解上具有高阶精度,但在冲击波的影响域中收敛的阶数减小了。

更新日期:2020-06-30
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