On a coupled elastic-fluid problem with a moving boundary

The numerical solution of a fracture propagating through a homogeneous elastic material by fluid injection is presented. As an example, the so-called PKN model [1-3] of a hydraulic fracture with an elliptic cross section propagating with a Newtonian fluid is investigated. The key elements in the solution are: coupled solid and fluid equations and the tracking of the fracture tip. The fracture tip's moving boundary is modeled on a fixed grid, using a Volume of Fluid method [4]. Numerical predictions of the fracture front, fracture opening, and net pressure compare well with analytical solutions.