A purely meshless implementation of SPH (Smoothed Particle Hydrodynamics) is investigated to validate the accuracy of SPH as a method for fully meshless computations of Taylor vortex flows, i.e. without the need for any particle re-meshing. The continuity and Navier-Stokes equations together with appropriate initial and boundary conditions, as well as an equation of state, are solved for water using purely meshless SPH, i.e. in which no re-meshing of smoothed particles is employed. The exact analytical unsteady solution is compared with the SPH computational results and good agreement is found. The results show that it is not necessary to employ particle re-meshing, which had previously been claimed to be an essential ingredient for SPH simulations of Taylor vortex flows. In the present purely meshless SPH simulations, regular as well as irregular initial distributions of smoothed particles are investigated with the minimum inter-particle spacing scale and maximum interparticle void scale monitored as functions of time to ensure limited particle clustering, spreading, and void formation. Our results show convergence of the computed solution to the analytical solution, with increasing number of the smoothed particles and with decreasing time step. In our computations, the highest-order derivatives corresponding to the viscous terms are directly computed, i.e. without any artificial viscosity. These findings suggest the utility of this approach as a promising tool for purely meshless SPH direct numerical simulations and large-eddy simulations of turbulent flows.
Some bifurcation diagrams for Taylor vortex flows
