For problems of convection–diffusion type, Eulerian–Lagrangian localized adjoint methods
provide a methodology that maintains the accuracy and efficiency of Eulerian–Lagrangian …

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 …

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 …

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

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

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 …

Many numerical methods for systems of convection–diffusion equations are based on an
operator splitting formulation, where convective and diffusive forces are accounted for in …

In this paper, we propose and analyze the mass-conservative characteristic finite difference
method for solving two-sided space-fractional advection-diffusion equation. The …