A random choice scheme for scalar advection

Abstract

SummaryThis paper is dedicated to a numerical method based on a random choice as proposed in Glimm's scheme. It is applied to the problem of advection of a scalar quantity. The numerical scheme proposed here relies on a fractional step approach for which: the first step is performed using any classical finite‐volume scheme, and the second step is a cell‐wise update. This second step is a projection based on a random choice. The resulting scheme possesses a very low level of numerical diffusion. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh‐size. The algorithm performs very well on one‐dimensional and multi‐dimensional problems. This algorithm is very easy to implement even for multi‐processor computations.