In this paper, a bilinear three-point fourth-order compact operator is applied to solve the two-
dimensional (2D) Sobolev equation with a Burgers' type nonlinearity. In order to derive a …

This paper proposes a fully implicit numerical scheme for immiscible incompressible two-
phase flow in porous media taking into account gravity, capillary effects, and heterogeneity …

In this work, we study the behavior of saturation fronts for two‐phase flow through a long
homogeneous porous column. In particular, the model includes hysteresis and dynamic …

We investigate the one-dimensional non-equilibrium Richards equation with play-type
hysteresis. It is known that regularized versions of this equation permit traveling wave …

We propose and analyse numerical schemes for a system of quasilinear, degenerate
evolution equations modelling biofilm growth as well as other processes such as flow …

We discuss two linearization and domain decomposition methods for mathematical models
for two-phase flow in a porous medium. The medium consists of two adjacent regions with …

Multiphase flow through porous media plays an important role in many practical
applications, from groundwater modelling, oil and gas recovery to CO2 sequestration. In the …

Flow and transport processes in porous media are relevant for a huge variety of applications
covering all areas of modern society. To describe and predict the relevant processes, it is …

We study several iterative methods for fully coupled flow and reactive transport in porous
media. The resulting mathematical model is a coupled, nonlinear evolution system. The flow …

The paper proposes a hybrid numerical method for solving a model problem of two-phase
nonequilibrium flow of an incompressible fluid in a porous medium. This problem is relevant …