Smoothed particle hydrodynamics model for flow through porous media

This paper presents the first application of Smoothed Particle Hydrodynamics (SPH) to problems in geomechanics. Originally developed for astrophysics applications, SPH is extended to model incompressible flows of moderate to low Reynolds numbers as encountered in groundwater flow systems. For such flows, modification of the standard SPH formalism is required to minimize errors associated with the use of a quasi-incompressible equation of state. Treatment of viscosity, state equation, kernel interpolation, and boundary conditions are described. Simulations using the method show close agreement with series solutions for Couette and Poiseuille flows. The model is demonstrated for two-dimensional flow through an idealized porous medium. The relationship between discharge velocity and hydraulic gradient is presented, and the corresponding value of hydraulic conductivity is computed.