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Abstract <p>The discontinuous particle method (DPM) is a method for modeling large systems based on a Lagrangian description. The method consists of two main stages: predictor and corrector. The density is chosen as the key particle characteristic. This article presents an improved method with particle “birth and death.” The algorithm correctly reproduces a nonsmooth analytical test (unrealistic from the point of view of physics). Limiters are not used. The proposed DPM implementation is illustrated at widely known examples for numerical modeling of fluid dynamic problems: the gradient catastrophe problem for the inviscid Burgers equation and Bore propagation and Dam-break problem for shallow water equations.</p>

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Discontinuous Particle Method in Shallow Water Problems

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • S. V. Bogomolov,
  • I. A. Panferova

摘要

Abstract

The discontinuous particle method (DPM) is a method for modeling large systems based on a Lagrangian description. The method consists of two main stages: predictor and corrector. The density is chosen as the key particle characteristic. This article presents an improved method with particle “birth and death.” The algorithm correctly reproduces a nonsmooth analytical test (unrealistic from the point of view of physics). Limiters are not used. The proposed DPM implementation is illustrated at widely known examples for numerical modeling of fluid dynamic problems: the gradient catastrophe problem for the inviscid Burgers equation and Bore propagation and Dam-break problem for shallow water equations.