Conference Dates

June 22-27, 2014


This article studies fluid flows through an unsaturated porous matrix, modeled under a mixture theory viewpoint, which give rise to nonlinear hyperbolic systems. An alternative procedure is employed to simulate these nonlinear nonhomogeneous hyperbolic systems of two partial differential equations representing mass and momentum conservation for the fluid (liquid) constituent of mixture. An operator splitting technique is employed so that the nonhomogeneous system is split into a time-dependent ordinary portion and a homogeneous one. This latter is simulated by employing Glimm’s scheme and an approximate Riemann solver is used for marching between two consecutive time steps. This Riemann solver conveniently approximates the solution of the associated Riemann problem by piecewise constant functions always satisfying the jump condition – giving rise to an approximation easier to implement with lower computational cost. Comparison with the standard procedure, employing the complete solution of the associated Riemann problem for implementing Glimm’s scheme, has shown good agreement.