Author(s)

G. Kosec & B. Šarler

Abstract

In the present paper, the recently developed local meshfree method solution of thermo-fluid problems is modified from the collocation to the combined collocation and weighted least squares approach and upgraded with an h-adaptive strategy. A one domain enthalpy formulation is used for modelling the solid-liquid energy transport and the liquid phase is assumed to behave as an incompressible Newtonian fluid modelled by the Boussinesq hypothesis. The involved temperature, enthalpy, velocity and pressure fields are represented on overlapping local sub-domains through weighted least squares approximation (by a truncated Gaussian weight in the domain nodes) and collocation (at the boundary nodes) by using multiquadrics Radial Basis Functions (RBF). The transport equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively through a novel local pressure correction algorithm. The node adaptivity is established through a phase-indicator and a node refinement strategy that takes into account the dynamic number of neighbouring nodes. The proposed approach is used to solve the standard Gobin Le Quéré melting benchmark with tin at Stefan number (Ste) 0.01, Prandtl number (Pr) 0.02, and Rayleigh number (Ra) 2.5e4. The node distribution changes through the simulation as the melting front advances. The solid is consequently computed at much lower node distribution density in comparison with the liquid, which speeds up the simulation and at the same time preserves accuracy. The latter issue has been demonstrated by comparison with the results of other combinations of numerical methods and formulations that attempted this benchmark in the past. Keywords: meshfree, RBF, weighted least squares, collocation, convectivediffusive problems, adaptation, refinement, melting, fluid flow, Newtonian fluids.

Keywords

meshfree, RBF, weighted least squares, collocation, convectivediffusive problems, adaptation, refinement, melting, fluid flow, Newtonian fluids