关于正则化显式有限差分方案在1D等熵气体动力学方程中弱保守条件的条件
On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations
AI总结：
本文研究了正则化显式有限差分方案在1D等熵气体动力学方程中弱保守性的条件，推导了CFL型准则并验证其与数值结果的一致性。
摘要：
我们考虑用于求解1D等熵气体动力学方程的显式双级三点空间有限差分方案。这些方案基于系统特有的准气体动力学和准流体动力学正则化。我们对常数解进行线性化，并推导出von Neumann型必要条件和CFL型准则（必要且充分条件）以保证对应初始值问题在整个实线上$ L^2 $意义下的弱保守性。该准则本质上比必要条件更狭窄，比最近在特定情况下获得的充分条件更广泛；此外，它最符合原始气体动力学系统的数值结果。
英文摘要：
We consider explicit two-level three-point in space finite-difference schemes for solving 1D barotropic gas dynamics equations. The schemes are based on special quasi-gasdynamic and quasi-hydrodynamic regularizations of the system. We linearize the schemes on a constant solution and derive the von Neumann type necessary condition and a CFL type criterion (necessary and sufficient condition) for weak conservativeness in $L^2$ for the corresponding initial-value problem on the whole line. The criterion is essentially narrower than the necessary condition and wider than a sufficient one obtained recently in a particular case; moreover, it corresponds most well to numerical results for the original gas dynamics system.
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