Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

In this paper, we study the unconditional convergence and error estimates of a Galerkin-
mixed FEM with the linearized semi-implicit Euler scheme for the equations of …

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

We discuss a numerical modeling to approximate a two-phase flow in a heterogeneous
porous media taking into account effects of dynamic capillary pressure. The governing …

Abstract Eulerian-Lagrangian and Modified Method of Characteristics (MMOC) procedures
provide computationally efficient techniques for approximating the solutions of transport …

The MMOC procedure for approximating the solutions of transport-dominated diffusion
problems does not automatically preserve integral conservation laws, leading to (mass) …

We present a new finite element (FE) method for magnetotelluric modelling of three-
dimensional conductivity structures. Maxwell's equations are treated as a system of first …

This paper presents results for the effect of surfactants on the dissolution rate of bubbles.
Most of the results to be presented are for carbon dioxide bubbles. However, a few results …

We use high resolution Monte Carlo simulations to study the dispersive mixing in two-phase,
immiscible, porous media flow that results from the interaction of the nonlinearities in the …

Chemical enhanced oil recovery by surfactant–polymer (SP) flooding has been studied in
two space dimensions. A new global pressure for incompressible, immiscible …