Several experiments have evidenced the occurrence of saturation overshoots for flows in homogeneous porous media. Such phenomena are ruled out by standard mathematical models, which are based on equilibrium assumptions. In this presentation we discuss nonequilibrium models, in particular including dynamic effects in the capillary pressure. This leads to extensions of the classical Buckley-Lever...

This paper presents a Buckley-Leverett analytical solution for non-Darcy displacement of two immiscible fluids in porous media. The multiphase non-Darcy displacement is described using a Forchheimer equation or other non-Darcy flow correlations under multiphase flow conditions. The analytical solution is used to obtain some insight into the physics of displacement involving non-Darcy flow effec...

A recently introduced scheme for networked conservation laws is analyzed in various experiments. The makes use of a novel relaxation approach that governs the coupling conditions network and does not require solution Riemann problem at nodes. We numerically compare dynamics obtained by to solutions using classical condition. In particular, we investigate case two outgoing edges Lighthill–Whitha...

In this paper, we present an intensive investigation of the finite volume method (FVM) compared to difference methods (FDMs). order show main in way approaching solution, take Burgers equation and Buckley–Leverett as examples simulate previously mentioned methods. On one hand, results using schemes Lax–Friedrichs Lax–Wendroff. other apply Godunov’s scheme method. Moreover, how starting with a v...