We propose a multiple relaxation time entropic realization of two-phase flow lattice Boltzmann model we introduced in earlier works arXiv:2112.01975 S.A. Hosseini, B. Dorschner, and I. V. Karlin, arXiv preprint, (2021). While the original with single allows us to reach large density ratios, it is limited terms stability respect non-dimensional viscosity Courant--Friedrichs--Lewy number. Here sh...

The present paper surveys important results in the theory of network flows which are not included in the book "Flows in Networks" by Ford and Fulkerson. The survey is divided into three areas: 1. Shortest paths and minimal cost flows, 2. Multi-terminal flows, 3. Multi-commodity flows.

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn–Hilliard–Navier–Stokes model introduced by Abels, Garcke and Grün (Math. Models Methods Appl. Sci. 2012), which uses a volume averaged velocity, we derive a diffuse interface mo...

The Galerkin Finite-Element Method using bilinear basis functions (in two dimensions) offers many advantages in the numerical treatment of flow through porous media. A significant disadvantage of this approach, however, is the lack of an explicit discrete requirement of conservation of mass on mesh cells. While this shortcoming is a concern in the case of single-phase flows, it is critical in t...