During recent years the authors and collaborators have been involved in an activity related
to the construction and analysis of large time step operator splitting algorithms for the …

Many numerical methods use characteristic analysis to accommodate the advective
component of transport. Such characteristic methods include Eulerian-Lagrangian methods …

The book has grown out of a concerted research effort over the last decade. We have
enjoyed collaboration with many good friends and colleagues on these problems, in …

We give a brief summary of numerical methods for time-dependent advection-dominated
partial differential equations (PDEs), including first-order hyperbolic PDEs and nonstationary …

A numerical algorithm for simulation of two‐phase flow in porous media is presented. The
algorithm is based on a modified Picard linearization of the governing equations of flow …

We present new approaches to reservoir modeling and flow simulation that dispose of the
pillar-grid concept that has persisted since reservoir simulation began. This results in …

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-
dimensional advection-diffusion equations with all combinations of inflow and outflow …

An adaptive local mesh refinement algorithm originally developed for unsteady gas
dynamics by MJ Berger is extended to incompressible flow in porous media. Multilevel …

Fractional flow formulations of the multi-phase flow equations exhibit several attractive
attributes for numerical simulations. The governing equations are a saturation equation …

We develop a family of Eulerian–Lagrangian localized adjoint methods for the solution of the
initial-boundary value problems for first-order advection-reaction equations on general multi …