Axisymmetric viscous incompressible flow simulation by using the Particle finite element PFEM-2 method in the open source Kratos code

In this paper, the particle finite element method (PFEM-2) for the simulation of the axisymmetric flows of a viscous incompressible fluid is considered. The necessary equations for the description of the axisymmetric flows by using the particle finite element method with some assumptions were obtained. The numerical model for solving axisymmetric flows of a viscous incompressible fluid was implemented in the Kratos open-source code on the basis of the existing application for solving two-dimensional problems. The numerical model for the simulation of the axisymmetric flows of a viscous incompressible fluid was validated on two problems. First of them is the Poiseuille problem about viscous flow in the pipe. The numerical solution obtained by particle finite element method are in the satisfactory agreement with the analytical solution for this problem. The second test is a problem of a droplet impact onto a deep liquid pool with similar fluid. As the comparison with analytical results is impossible, the results of particle finite element method simulation were compared with results of the numerical simulation obtained by using the open-source package Gerris (Volume of Fluid method). The results of comparing of numerical simulations of droplet impact onto a liquid pool obtained by two different codes also in satisfactory agreement.