The Conservative Random Choice Method for the Numerical Solution of the Advection Equation

Abstract

A version of the random choice method (RCM), which we call the conservative random choice method (CRCM), is introduced to solve the variable coefficient linear advection equation. CRCM is an advection scheme that does not create numerical diffusion nor dispersion, enabling it to preserve initial conditions, discontinuities, and other nonsmooth features. It is capable of handling the variable coefficients case without creating or destroying mass, as is the case of the original RCM. These properties make CRCM a useful scheme for applications such as atmospheric and water transport.