An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems (Communications in Computational Physics, 2020)
In this paper, a diffuse-interface immersed boundary method (IBM) is proposedto treat three different thermal boundary conditions (Dirichlet, Neumann, Robin)in thermal flow problems. The novel IBM is implemented combining with the latticeBoltzmann method (LBM). The present algorithm enforces the three types of thermalboundary conditions at the boundary points. Concretely speaking, the IBM for theDirichlet boundary condition is implemented using an iterative method, and its mainfeature is to accurately satisfy the given temperature on the boundary. The Neumannand Robin boundary conditions are implemented in IBM by distributing the jump ofthe heat flux on the boundary to surrounding Eulerian points, and the jump is obtainedby applying the jump interface conditions in the normal and tangential directions. Asimple analysis of the computational accuracy of IBM is developed. The analysis indicatesthat the Taylor-Green vortices problem which was used in many previous studiesis not an appropriate accuracy test example. The capacity of the present thermal immersedboundary method is validated using four numerical experiments: (1) Naturalconvection in a cavity with a circular cylinder in the center; (2) Flows over a heatedcylinder; (3) Natural convection in a concentric horizontal cylindrical annulus; (4) Sedimentationof a single isothermal cold particle in a vertical channel. The numericalresults show good agreements with the data in the previous literatures.