Parallel adaptive solution of coupled Rayleigh-Bénard-Marangoni problems with the Navier-slip. (English) Zbl 1328.76044
Summary: This study deals with modeling certain nonlinear interactions that give rise to cellular flow in heated thin fluid layers with thermocapillary surface-tension at the free surface. Of particular interest in these Rayleigh-Bénard-Marangoni studies is the effect of varying roughness (stick and slip) on the base or sides of the fluid container. This stick-slip behavior at container boundaries and thermocapillary shear stress at the free surface may lead to strongly varying local gradients in the solution that are addressed here using local adaptive mesh refinement. In turn, these local effects influence the global structure of cell patterns resulting from competing buoyancy, surface-tension and stick-slip effects. This behavior is illustrated by the results of numerical simulations of cellular flow structure in containers of varying aspect ratio and with spatially varying base boundary treatments. Details of the Navier-slip approximation and the adaptive mesh refinement strategy are given, together with a brief description of the relevant features of the parallel adaptive software framework, LibMesh, and associated algorithms employed in the present simulations.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76R10 | Free convection |
| 76D45 | Capillarity (surface tension) for incompressible viscous fluids |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
| 65Y05 | Parallel numerical computation |
Keywords:
natural convection; adaptive finite elements; stick-slip behavior; thermocapillary shear stress; cellular flow structureReferences:
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