Grid-Free Vortex Methods for Natural Convection; Handling Source Terms and Nonlinear Diffusion

Abstract

Vortex methods for simulating natural convection of a ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low Mach number flows. In solving the linear system governing the redistribution of a given element, the entropy of the fractions transferred to its neighbors is maximized. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in nonreacting buoyancy-driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1,562.5 to 25,000 are presented.