Continuity equation and vacuum regions in compressible flows

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

Population genetics in compressible flows.

We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field and fitness advantage, number fluctuations lead to a coarsening dynamics typical of the stochastic Fisher equation. We investigate three examples of compres...

Modelling Compressible Multiphase Flows

We give in this paper a short review of some recent achievements within the framework of multiphase flow modeling. We focus first on a class of compressible two-phase flow models, detailing closure laws and their main properties. Next we briefly summarize some attempts to model two-phase flows in a porous region, and also a class of compressible three-phase flow models. Some of the main difficu...

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible...

Krylov Methods for Compressible Flows

In this paper we investigate the application of Krylov methods to compressible ows, and the e ect of implicit boundary conditions on the implicit solution of nonlinear problems. Two defect-correction procedures, namely, Approximate Factorization (AF) for structured grids, and ILU/GMRES for general grids are considered. Also, considered here, is Newton-Krylov matrix-free methods that we combine ...