A mixed finite element approximation for Darcy-Forchheimer flows of slightly compressible fluids
Provides a numerical framework for a nonlinear degenerate system in porous media flow, but the problem is domain-specific and the method is an incremental extension of existing mixed finite element techniques.
The paper develops a mixed finite element method for Darcy-Forchheimer flows of slightly compressible fluids, proving stability and error estimates with numerical experiments confirming convergence rates.
In this paper, we consider the generalized Forchheimer flows for slightly compressible fluids in porous media. Using Muskat's and Ward's general form of Forchheimer equations, we describe the flow of a single-phase fluid in $\mathbb R^d, d\ge 2$ by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.