A new implicit fictitious domain method for the simulation of flow in complex geometries with heat transfer

A numerical algorithm for the simulation of flow past immersed objects with heat transfer is proposed and validated which conforms with the ideas of the fictitious domain method. A momentum source term is added to account for the presence of the object and a heat source term is proposed to impose the Dirichlet boundary condition on the surface of the objects. The algorithm is an implicit fictitious domain based method where the entire fluid-immersed object domain assumed to be an incompressible fluid. The flow domain is constrained to be divergence free, whereas a rigidity constraint is imposed on the body domain. Heat transfer is similarly considered by assuming that the object domain is filled with a fluid with different thermal properties. The SIMPLE algorithm with a collocated grid arrangement is used for pressure–velocity coupling which is unconditionally stable. The algorithm is validated by considering stationary, forced motion and freely moving objects with both isothermal and freely variable temperature inside the object. Good agreement with previous numerical and experimental studies for all the test cases is observed.