A Hyperbolic-Elliptic Model Problem for Coupled Surface-Subsurface Flow

作者：Magiera Jim; Rohde Christian; Rybak Iryna

来源：Transport in Porous Media, 2016, 114(2): 425-455.

DOI：10.1007/s11242-015-0548-z

• Free flow
• Porous medium
• Coupling
• Kinematic wave equation
• Brinkman's equations
• Vanishing viscosity limit

We consider a model problem for coupled surface-subsurface flow. The model consists of a nonlinear kinematic wave equation for the surface fluid's height and a Brinkman model that governs fluid velocity and pressure for subsurface dynamics. For this coupled hyperbolic-elliptic model we establish the existence of weak solutions. The proof is based on a viscous approximation and the method of compensated compactness by virtue of appropriate energy estimates. To solve the coupled problem numerically, a finite volume method is applied. The numerical scheme is used to illustrate the influence of the Brinkman parameter on the coupled flow pattern for infiltration scenarios.

• 出版日期2016-9