A hybrid computer simulation approach to shock propagation in fluid through porous media

An interacting lattice gas method is introduced to study the shock propagation through fluid in a porous medium. this approach incorporates the collision between the fluid particles as in direct simulation methods and interactions among the particles by the Metropolis algorithms to hop the fluid particles. We consider a two dimensional discrete lattice with a line of shock in a porous medium generated by a random distribution of fixed barriers at the pore boundaries. The velocity gradient caused by the shock drives the fluid. We find that the shock fronts drift in high porosity and propagate nondiffusively as the shock-driven flow field competes with the pore barriers, especially at low porosity (i.e. high ramification). The magnitude of the fluid velocity at the shock front decays with time nonlinearly. The shock depletes the fluid density as it propagates into the lattice. Damping of the shock profile is enhanced on reducing the porosity.