Accurate discretization of advection-diffusion equations

Accurate discretization of advection-diffusion equations.

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advecti...

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,...

Nonlocal nonlinear advection-diffusion equations

We review some results about nonlocal advection-diffusion equations based on lower bounds for the fractional Laplacian. To Haim, with respect and admiration.

Discretization Methods with Analytical Characteristic Methods for Advection-diffusion-reaction Equations and 2d Applications

Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convectiondiffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerica...

Numerical Solution of Advection-Diffusion-Reaction Equations