Author(s)

C. Golia & B. Buonomo

Abstract

Vortex and thermal blob methods recently conceived by the authors to solve the coupled momentum and energy equations in thermal free convection unsteady problems, is updated here, with the use of a self-optimized FMM methodology, to compute the velocity from the vorticity field. Instead of the usual O(N2) needed for full direct computations, this approximate method requires for N blob particles to use only O(N) operations. The reduced computing time allows detailed analysis of long term, large flow field for problems having Grashoff numbers of realistic magnitude, even with the use of modern PCs. After the presentation of the method, preliminary tests are discussed to ascertain the accuracy of the results and to test the use and performances with classical problems of interest. Keywords: vortex and thermal blob methods, particle-based lagrangian method, unsteady flows, buoyant heat transfer, thermal plume. 1 Introduction Even if vortex blobs methods have been extensively used for forced convection viscous problems, see [1] for a wide review, scant attention has been posed on natural thermal convection problems. Indeed vortex methods automatically assume the asymptotic vanishing of vorticity, so if ones combine vortex and thermal blobs, the resultant method will be ideally apt to solve fluid buoyant/mixed problems in free space such as plumes, fires and geostrophic flows, etc. without having to deal with the cumbersome pressure closure problem.

Keywords

vortex and thermal blob methods, particle-based lagrangian method, unsteady flows, buoyant heat transfer, thermal plume.