Grid Free Lagrangian Blobs Vortex Method with Brinkman Layer Domain Embedding Approach for Heterogeneous Unsteady Thermo Fluid Dynamics Problems

Modeling unsteady thermal–viscous flows inside/around complicated geometriescontaining multiphase sub-systems (fluid–porous–solid) and multi-physicsphenomena (diffusion; forced/free/mixed convection; time variations of velocity,temperatures and heat fluxes sources; still and moving bodies) is an ambitiouschallenge in many applications of interest in science and engineering. Scope ofthis exploratory work is to investigate if the combination of a grid free LagrangianBlob method with a Brinkman layer domain embedding approach can be usefulfor the preliminary analysis of heterogeneous unsteady thermal buoyantproblems, where easiness, readiness, short computational times, goodqualitative and sufficient quantitative accuracy are the most important aspects. Inthis work we couple a grid free unsteady Lagrangian Thermal-Vortex Blobmethod with a double penalization method that considers solid bodies contouredby a fictitious buffer thin boundary layer, described by a porous Brinkman model.The model problem in this study is the interaction of a thermal buoyant plumewith a solid body, still or in motion. Both solid body and Brinkman boundary layerare described by volume penalization applied by an unsteady mask method.After a description of this novel approach, preliminary analyses for validations arepresented for various thermal buoyant steady/unsteady problems relative tothermal and thermal-vortical patches, fixed, free and in presence of a still ormoving body. Comments on pros, contras and further work, conclude the paper.