This paper is dedicated to a numerical method based on Glimm's idea and applied to the specific problem of advection of an indicator function. The numerical scheme relies on a fractional step approach for which: the first step is performed using any classical finite-volume scheme, and the second step sharpens the approximated solution issued from the first step. This second step is based on a random choice as proposed in the original idea of Glimm. In order to assess the capabilities of this approach, several test cases have been investigated including convergence studies with respect to the mesh-size. Since the method proposed in this paper naturally extends to multi-dimensional domain, both one- and two-dimensional cases have been considered.

中文翻译：

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类 Glimm 格式在多维域传输方程中的应用

本文致力于一种基于 Glimm 思想的数值方法，并应用于指标函数对流的具体问题。数值方案依赖于分步法，其中：第一步使用任何经典的有限体积方案执行，第二步锐化从第一步发出的近似解。第二步是基于 Glimm 最初想法中提出的随机选择。为了评估这种方法的能力，已经研究了几个测试案例，包括关于网格大小的收敛性研究。由于本文提出的方法很自然地扩展到多维领域，因此一维和二维情况都被考虑了。