A Semi-implicit Generalized Finite Differences Approach to Simulate Natural Convective Viscous Flows

The purpose of this work is to carry out a Lagrangian semi-implicit Generalized Finite Differences (GFDM) implementation to simulate transient natural convective viscous flows. The solution of the incompressible Navier–Stokes equations is formulated through the first order Chorin’s projection method whilst the energy equation is implicitly discretized with the first order Euler scheme. The semi-implicit set of discretized equations is solved with the Finite Point set Method where the incorporation of the boundary conditions is done in a direct and simple manner without requiring any special treatment or stabilization. The main features behind this mesh free approach as well as details of its implementation are shown. The suitability and the accuracy of this approach for the numerical simulation of the transient natural convective viscous flows are demonstrated through the solution of the two-dimensional benchmark problem. Finally, the stability of this FPM approach is studied through the variation of parameters in the two-dimensional benchmark problem, which shows that this formulation is a promising numerical tool for the simulation of the processes involving convective thermal flows.