An immersed boundary-body conformal enrichment method for thermal flow problems

Solving the flow around objects with complex shapes may involve extensive meshing work that has to be repeated each time a change in the geometry is needed. The same problem arises if one need to solve the heat transfer involving multiple materials whose interface is complex or changes with time. Time consuming meshing can be avoided when the solution algorithm can tackle grids that do not fit the shape of the interface between different materials. This work presents the extension of a recently proposed immersed boundary-body conformal enrichment (IB-BCE) method to the solution of the heat transfer. The method produces solutions of the temperature field satisfying accurately the continuity of the normal heat flux at interfaces between materials with different thermal properties. As for the isothermal flow problems, the fluid/solid interface is defined using a level-set function and the finite element discretization of interface elements is enriched with additional degrees of freedom which are eliminated at element level. The method is first validated in the case of heat conduction in two solids with different thermal properties. Then, solutions are shown for the more complex conjugate heat transfer between water and aluminum for two configurations: steady state flow inside a channel obstructed by a heated cylinder and transient flow around a heated cylinder. For each problem the solutions obtained using the proposed immersed boundary method are compared with solutions on body-conformal meshes having comparable mesh size distribution. The proposed approach is very accurate and effective in capturing the sharp discontinuity in the normal temperature gradient at the interface.