An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions

An ELLAM Scheme for Advection-Diffusion Equations in Two Dimensions

We develop an Eulerian–Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages o...

An ELLAM Scheme for Advection-Dispersion Equations in Two Dimensions

We develop an ELLAM (Eulerian-Lagrangian localized adjoint method) scheme to solve twodimensional advection-dispersion equations with all combinations of in ow and out ow Dirichlet, Neumann, and ux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantage...

An ELLAM Scheme for Advection-Di usion Equations in Multi-Dimensions

Advection-diiusion equations describe the transport of solutes in groundwater and surface water, the movement of aerosols and trace gases in the atmosphere, and many problems in other important applications. They often cause serious numerical diiculties. Classical space-centered or upwind numerical methods tend to yield numerical solutions with various combinations of excessive oscillations and...

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

An ELLAM Scheme for Multidimensional Advection-Reaction Equations and Its Optimal-Order Error Estimate