Visualization of Calculations of the Discontinuous Particle Method in Problems with Viscosity

Abstract

In previous studies, it was shown that the discontinuous particle method performs well in computational hydrodynamics problems with strong gradients, exemplified by the formation of an oblique stress jump. This article explores the application of the discontinuous particle method to problems involving viscosity. The investigation includes a one-dimensional Burgers' equation with an initial condition in the form of a smoothed wave and a two-dimensional Blasius problem. Numerical experiments showed agreement between the obtained solution and the analytical one. However, in the two-dimensional case, the algorithm's performance significantly decreases due to the need to determine particle neighbors. It is concluded that the discontinuous particle method can handle viscosity problems in one dimension, but modifications to the existing algorithm are required for higher-dimensional cases. The study of applying the discontinuous particle method to viscous problems was conducted as part of a comprehensive research effort comparing the relative accuracy of numerical methods on benchmark solutions.