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：

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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。