An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system

2020/05/16 by Xiaokai Huo, Huo, Xiaokai, Hailiang Liu +5
Computer Science · Mathematics · #35K55 #35L45 #35Q79 #65M06 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2005.08062

openalex publication_date 2020/05/16 · openalex created_date 2020/05/21 · openalex updated_date 2026/07/28

Abstract

We develop a new finite difference scheme for the Maxwell-Stefan diffusion system. The scheme is conservative, energy stable and positivity-preserving. These nice properties stem from a variational structure and are proved by reformulating the finite difference scheme into an equivalent optimization problem. The solution to the scheme emerges as the minimizer of the optimization problem, and as a consequence energy stability and positivity-preserving properties are obtained.

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

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