多孔介质方程和等熵欧拉方程组的变分粒子格式
Variational Particle Schemes for the Porous Medium Equation and for the System of Isentropic Euler Equations
AI总结：
基于最优传输理论，通过离散变分特征而非偏微分方程本身，提出了具有优异稳定性的新数值格式，成功捕捉等熵欧拉方程中的激波和稀疏波等非线性特征，并设计了高阶方法。
摘要：
多孔介质方程和等熵欧拉方程组都可以视为最优传输理论框架下概率测度适当流形上的最速下降。通过离散这些变分特征而非偏微分方程本身，我们获得了具有显著稳定性的新格式。我们展示了它们成功捕捉流动的非线性特征，例如等熵欧拉方程中的激波和稀疏波。我们还展示了如何在最优传输设置下，使用向后微分公式（BDF）多步法或对角隐式龙格-库塔方法为这些问题设计高阶方法。
英文摘要：
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction waves for the isentropic Euler equations. We also show how to design higher order methods for these problems in the optimal transport setting using backward differentiation formula (BDF) multi-step methods or diagonally implicit Runge-Kutta methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
