Geometrically exact time-integration mesh-free schemes for advection-diffusion problems derived from optimal transportation theory and their connection with particle methods

被引：6

作者：

Fedeli, L. ^{[1
]}

Pandolfi, A. ^{[2
]}

Ortiz, M. ^{[3
]}

机构：

[1] Univ Penn, Mech Engn & Appl Sci Dept, Philadelphia, PA 19104 USA

[2] Politecn Milan, Civil & Environm Engn Dept, I-20133 Milan, Italy

[3] CALTECH, Engn & Appl Sci Div, Pasadena, CA 91125 USA

来源：

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2017年 / 112卷 / 09期

基金：

美国国家科学基金会;

关键词：

optimal transportation; diffusion problems; time integrators; approximation theory; FOKKER-PLANCK EQUATION; APPROXIMATION SCHEMES; VARIATIONAL INTEGRATORS; CAHN-HILLIARD; HYDRODYNAMICS; ENERGY; FLOWS;

D O I：

10.1002/nme.5552

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We develop an optimal transportation mesh-free particle method for advection-diffusion in which the concentration or density of the diffusive species is approximated by Dirac measures. We resort to an incremental variational principle for purposes of time discretization of the diffusive step. This principle characterizes the evolution of the density as a competition between the Wasserstein distance between two consecutive densities and entropy. Exploiting the structure of the Euler-Lagrange equations, we approximate the density as a collection of Diracs. The interpolation of the incremental transport map is effected through mesh-free max-ent interpolation. Remarkably, the resulting update is geometrically exact with respect to advection and volume. We present three-dimensional examples of application that illustrate the scope and robustness of the method. Copyright (c) 2017 John Wiley & Sons, Ltd.

引用

页码：1175 / 1193

页数：19