An Energy Stable and Positivity-Preserving Scheme for the Maxwell--Stefan Diffusion System
Xiaokai Huo, Hailiang Liu, Athanasios E. Tzavaras, Shuaikun Wang · SIAM Journal on Numerical Analysis · 2021
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.