Научная визуализация, 2021, том 13, номер 2, страницы 94 - 103, DOI: 10.26583/sv.13.2.07

Visualization of the Application of the Discontinuous Particle Method without Taking into Account the Particle Shape to the Quasi-Linear Transport Equation

Авторы: S. V.  Bogomolov^1,A, A.E.  Kuvshinnikov^2,B

^A Moscow State University, Faculty of Computational Mathematics and Cybernetics

^B Keldysh Institute of Applied Mathematics RAS

¹ ORCID: 0000-0002-5414-6019, bogomo@cs.msu.su

² ORCID: 0000-0003-1667-6307, kuvsh90@yandex.ru

 

Аннотация

The paper considers a new variant of the discontinuous particle method. The main feature of the new variant is minimal smearing of discontinuities, due to the new criterion of rearrangement of particles. In contrast to the previously used variant with the analysis of overlaps of particles, which required an assumption about their shape, we use the key characteristic of particles, namely, their mass. The assumption is made that in nonlinear elastic transport not only the masses of the particles are conserved, but also the mass located between the centers of these particles. This requirement leads to the fact that a change of distance between particles in the process of their shear and conservation of mass in the space between them, lead to a change of density of one of the particles. The new version applies to solving the one-dimensional and two-dimensional quasi-linear transport equation problem. Visualization is used to monitor the numerical solution, showing that the shock velocity is calculated correctly, and the shock itself is smeared on one particle.

 

Ключевые слова: particle method, inviscid Burgers’ equation.