Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
Convergence of a Lagrangian discretization for barotropic fluids and porous media flow
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正压流体和多孔介质流拉格朗日离散化的收敛性
DOI：
10.1137/21m1422756
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
A. Natale
中科院分区：
文献类型：
--
作者：
T. Gallouët;Q. Mérigot;A. Natale
当用拉格朗日变量表示时，可压缩（正压）流体的运动方程具有经典哈密顿系统的结构，其中势能由流体的内能给出。这种系统的耗散对应物与多孔介质方程一致，可以将其以相同内能的梯度流的形式铸造。受这些相关变分结构的启发，我们针对这两个问题提出了一种粒子方法，其中内能被 L2 意义上的 Moreau-Yosida 正则化所取代，可以有效地计算为半离散最优传输问题。使用利用欧拉变量中问题的凸性的调制能量论证，我们证明了对平滑解的定量收敛估计。我们通过几次数值测试来验证这些估计。
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The dissipative counterpart of such a system coincides with the porous medium equation, which can be cast in the form of a gradient flow for the same internal energy. Motivated by these related variational structures, we propose a particle method for both problems in which the internal energy is replaced by its Moreau-Yosida regularization in the L2 sense, which can be efficiently computed as a semi-discrete optimal transport problem. Using a modulated energy argument which exploits the convexity of the problem in Eulerian variables, we prove quantitative convergence estimates towards smooth solutions. We verify such estimates by means of several numerical tests.
影响因子：
2
作者：
Franz, Tino;Wendland, Holger
通讯作者：
Wendland, Holger