A projection method for porous media flow

  title={A projection method for porous media flow},
  author={Nicholas J. Derr and Chris H. Rycroft},
Flow through porous, elastically deforming media is present in a variety of natural contexts rang-ing 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 di ffi cult to solve numerically, requiring nonlinear implicit solvers or flux-splitting methods. Here, we present… 

Figures from this paper



A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows

We present a numerical method for computing solutions of the incompressible Euler or Navier?Stokes equations when a principal feature of the flow is the presence of an interface between two fluids

Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents

This is a study of the formulation, some basic solutions, and applications of the Biot linearized quasistatic elasticity theory of fluid-infiltrated porous materials. Whereas most previously solved

Topology optimization of fluids in Stokes flow

We consider topology optimization of fluids in Stokes flow. The design objective is to minimize a power function, which for the absence of body fluid forces is the dissipated power in the fluid,

Reference map technique for incompressible fluid–structure interaction

The flapping analysis is extended beyond the thin-flag limit, revealing an additional destabilization mechanism to induce flapping and the method has several useful features including the able to model solids with sharp corners and the ability to model actuated solids.

Eulerian simulation of complex suspensions and biolocomotion in three dimensions

A three-dimensional computational method where both fluid and solid can be represented on a fixed computational grid, which simplifies the coupling between the two phases considerably and eliminates the need for meshing complex geometries typical in other FSI approaches.

Accurate projection methods for the incompressible Navier—Stokes equations

Abstract This paper considers the accuracy of projection method approximations to the initial–boundary-value problem for the incompressible Navier–Stokes equations. The issue of how to correctly

Saturated Elastic Porous Solids: Incompressible, Compressible and Hybrid Binary Models

Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a