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Discontinuous Particle Method for Diffusion Advection Problemsстатья
- Авторы: Bogomolov S.V., Panferova I.A.
- Журнал: Mathematical Models and Computer Simulations
- Том: 16
- Номер: Suppl.1
- Год издания: 2024
- Первая страница: 36
- Последняя страница: 47
- DOI: 10.1134/S2070048224700789
- Аннотация: The particle method is a numerical method for modeling large systems based on theirLagrangian description. The discontinuous particle method belongs to the “particle–particle” typeand consists of two main stages: predictor and corrector. At the predictor stage, particles move. At thecorrector stage, a partner for interaction is selected from among the neighbors of the particle, whichhas the greatest influence on the local dynamics of the system. The “discontinuity” lies in the methodof correcting the density of only one of the interacting particles. That is why the restoration of the distributiondensity occurs in the minimum region determined by only two selected particles, so the frontis smeared by only one particle. The novelty of our method is to choose the density as a major characteristicof the particle unless its shape. The criterion for the density reconstruction is the preservationof the projection of the mass 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 constructedusing two selected interacting particles, which allows us to reduce a two-dimensional problemto a one-dimensional one. The effectiveness of the method is presented using the Crowley test as anexample. Despite the linearity of this problem the trajectories of the particles are not simple. That’swhy we need the Runge–Kutta method at the predictor stage to increase the accuracy. Our Lagrangianapproach to constructing the particle method contrasts with another frequently used representative ofthe particle–particle method—the smoothed particle method (SPH). The article is of a methodologicalnature, its purpose is to demonstrate the capabilities of the new discontinuous particle method.
- Добавил в систему: Богомолов Сергей Владимирович