In past papers it has been shown that the discontinuous particle method copes well with computational fluid dynamics problems having a strong gradient, the problem of oblique stress jump formation being an example. This paper deals with the application of the discontinuous particle method to viscosity problems. In the study, a one-dimensional Burgers equation with an initial condition in the form of a smoothed wave and a two-dimensional Blasius problem were taken. Numerical experiments showed the correspondence of the obtained solution to the analytical one, but in the two-dimensional case the performance of the algorithm drops strongly due to the necessity to determine the neighbours of the particle. It is concluded that the discontinuous particle method can solve viscosity problems in the one-dimensional case, but modifications of the existing algorithm are required for higher dimensional cases. The application of the discontinuous particle method to viscous problems was studied as part of a general comprehensive study of the comparative accuracy of numerical methods on reference solution.

Discontinuous particle method, Burgers’ equation, computational gas dynamics, Blasius boundary layer

Bogomolov S.V.,  ,  orcid.org/0000-0002-5414-6019,  Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University

Kuvshinnikov Artyom Evgenyevich,  ,  orcid.org/0000-0003-1667-6307,  KIAM RAS