A Generalized Finite Volume Method for Density Driven Flows in Porous Media

Abstract

In this article, we consider a time evolution equation for solute transport, coupled with a pressure equation in space dimension 2. For the numerical discretization, we combine the generalized finite volume method SUSHI on adaptive meshes with a time semi-implicit scheme. In the first part of this article, we present numerical simulations for two problems: a rotating interface between fresh and salt water and a well-known test case proposed by Henry. In the second part, we also introduce heat transfer and perform simulations for a system from the documentation of the software SEAWAT.

Keywords

• porous media
• density driven flows
• finite volume methods
• the SUSHI scheme
• adaptive meshes
• heat transfer