This 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.

中文翻译：

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标量平流的随机选择方案

本文致力于研究 Glimm 方案中提出的基于随机选择的数值方法。它应用于标量的平流问题。这里提出的数值方案依赖于分数步方法，其中：第一步使用任何经典的有限体积方案执行，第二步是单元更新。第二步是基于随机选择的预测。由此产生的方案具有非常低的数值扩散水平。为了评估这种方法的功能，研究了几个测试用例，包括网格大小的收敛研究。该算法在一维和多维问题上都有很好的表现。即使对于多处理器计算，该算法也非常容易实现。