Lattice-Boltzmann and meshless point collocation solvers for fluid flow and conjugate heat transfer

The applicability and performance of the lattice-Boltzmann (LB) and meshless point collocation methods as CFD solvers in flow and conjugate heat transfer processes are investigated in this work. Lid-driven cavity flow and flow in a slit with an obstacle including heat transfer are considered as case studies. A comparison of the computational efficiency accuracy of the two methods with that of a finite volume method as implemented in a commercial package (ANSYS CFX, ANSYS Inc., Canonsburg, PA) is made. Utilizing the analogy between heat and mass transfer, an advection-diffusion LB model was adopted to simulate the heat transfer part of the slit flow problem followed by a rigorous mapping of the mass transfer variables to the heat transfer quantities of interest, thus circumventing the need for a thermal LB model. Direct comparison among the results of the three methods revealed excellent agreement over a wide range of Reynolds and Prandtl number values. Furthermore, an integrated computational scheme is proposed, utilizing the rapid convergence of the LB model in the flow part of the conjugate heat transfer problem with that of the meshless collocation method for the heat transfer part. The meshless treatment remains sufficiently rapid even for conduction-controlled processes in contrast to the LB method, which is very rapid in the convection-controlled case only. A single, common computational grid, composed of regularly distributed nodes is used, saving significant computational and coding time and ensuring convergence of the discrete Laplacian operator in the heat transfer part of the computations.