A projection method for porous media flow

06/29/2022
by   Nicholas J. Derr, et al.
0

Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange multiplier to satisfy the resulting constraint on fluid divergence. The resulting system of equations is a possibly non-linear saddle-point problem and difficult to solve numerically, requiring nonlinear implicit solvers or flux-splitting methods. Here, we present a method for the simulation of flow through porous media and its coupled elastic deformation. The pore pressure field is calculated at each time step by correcting trial velocities in a manner similar to Chorin projection methods. We demonstrate the method's second-order convergence in space and time and show its application to phase separating neo-Hookean gels.

READ FULL TEXT

page 12

page 13

research
12/08/2021

A decoupled numerical method for two-phase flows of different densities and viscosities in superposed fluid and porous layers

In this article we consider the numerical modeling and simulation via th...
research
01/06/2022

A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Magnetohydrodynamics Equations

We introduce a new hybridized discontinuous Galerkin method for the inco...
research
12/21/2019

A high-order discontinuous Galerkin pressure robust splitting scheme for incompressible flows

The accurate numerical simulation of high Reynolds number incompressible...
research
12/29/2020

Efficient Solvers for Nonstandard Models for Flow and Transport in Unsaturated Porous Media

We study several iterative methods for fully coupled flow and reactive t...
research
04/15/2020

A novel pressure-free two-fluid model for one-dimensional incompressible multiphase flow

A novel pressure-free two-fluid model formulation is proposed for the si...
research
01/27/2021

Multigrid reduction preconditioning framework for coupled processes in porous and fractured media

Many subsurface engineering applications involve tight-coupling between ...

Please sign up or login with your details

Forgot password? Click here to reset