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Abstract <p>The particle method is a numerical method for modeling large systems based on their Lagrangian description.</p> <p>The discontinuous particle method belongs to the ‘‘particle-particle’’ type and consists of two main stages:predictor and corrrector. At the predictor stage, the particles shift. At the corrector stage, a partner for interaction is selected among the particle’s neighbors, which has the greatest influence on the local dynamics of the system. The ‘‘discontinuity’’ lies in the method of correcting the density of only one of the interacting particles. That is why the restoration of the distribution density occurs in a minimal region determined by only two selected particles, which leads to the ‘‘smearing’’ of the front by only one particle.</p> <p>The novelty of the presented method is to choose the density as a major characteristic of the particle unless its shape. The criterion for the density reconstruction is the preservation of the mass projection on the plane passing through the centers of mass of the interacting particles. A neighbor for density correction is selected using the ‘‘impact parameter’’. The density is constructed using two selected interacting particles, which makes it possible to reduce a two-dimensional problem to a one-dimensional one.</p> <p>A significant advantage of this algorithm is the absence of limiters.</p> <p>The efficiency of the method is demonstrated using the Crowley test as an example. Despite the linearity of the problem, the particle trajectories are complex: the neighbors of the particle are constantly changing. It is shown that the Runge–Kutta method at the predictor stage significantly increases the accuracy of the numerical solution.</p> <p>Our Lagrangian approach to constructing the particle method contrasts with another frequently used ‘‘particle–particle’’ method—the smoothed particle method (SPH).</p>

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One Test for the Discontinuous Particle Method in Convection Problems

  • 期刊论文

  • 发表日期：

    2025年9月3日

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

摘要

Abstract

The particle method is a numerical method for modeling large systems based on their Lagrangian description.

The discontinuous particle method belongs to the ‘‘particle-particle’’ type and consists of two main stages:predictor and corrrector. At the predictor stage, the particles shift. At the corrector stage, a partner for interaction is selected among the particle’s neighbors, which has the greatest influence on the local dynamics of the system. The ‘‘discontinuity’’ lies in the method of correcting the density of only one of the interacting particles. That is why the restoration of the distribution density occurs in a minimal region determined by only two selected particles, which leads to the ‘‘smearing’’ of the front by only one particle.

The novelty of the presented method is to choose the density as a major characteristic of the particle unless its shape. The criterion for the density reconstruction is the preservation of the mass projection on the plane passing through the centers of mass of the interacting particles. A neighbor for density correction is selected using the ‘‘impact parameter’’. The density is constructed using two selected interacting particles, which makes it possible to reduce a two-dimensional problem to a one-dimensional one.

A significant advantage of this algorithm is the absence of limiters.

The efficiency of the method is demonstrated using the Crowley test as an example. Despite the linearity of the problem, the particle trajectories are complex: the neighbors of the particle are constantly changing. It is shown that the Runge–Kutta method at the predictor stage significantly increases the accuracy of the numerical solution.

Our Lagrangian approach to constructing the particle method contrasts with another frequently used ‘‘particle–particle’’ method—the smoothed particle method (SPH).