A random-choice scheme for scalar advection

Résumé de l'exposé

The talk 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.

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