Immersed boundary methods for heat transfer

Purpose - The purpose of this paper is to present two different methods for the imposition of thermal boundary conditions (BCs) in the framework of two-phase flows: an immersed boundary method (IBM) and a Ghost cell method. Both methods are able to handle Dirichlet as well as Neumann BCs.
Design/methodology/approach - Direct numerical simulations of two-phase flows are performed where the thermal BCs at the phase boundary is accounted for with two different approaches.
Findings - Both methods are validated with the results obtained on a body-fitted mesh. Simulations of the three-dimensional flow and temperature field around a sphere demonstrate versatility and accuracy of both methods.
Originality/value - This is the first time Neumann BCs are imposed by means of an IBM with a direct heating approach employing regularized delta functions. The test cases considered may also serve as benchmarks for other studies.

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