Consistent Robin boundary enforcement of particle method for heat transfer problem with arbitrary geometry

Abstract Enforcing accurate and consistent boundary conditions is a difficult issue for particle methods, due to the lack of information outside boundaries. Recently, consistent Neumann boundary condition enforcement is developed for the least squares moving particle semi-implicit method (LSMPS). However, the Robin boundary cannot be straightforwardly considered by that method because no computational variables are defined on the wall boundary. In this paper, a consistent Robin boundary enforcement for heat transfer problem is proposed. Based on the Taylor series expansion, the Robin boundary condition for temperature is converted to the fitting function of internal rather than boundary particles and incorporated into least squares approach for discretization schemes. Arbitrary geometric wall as well as free surface boundary can be easily treated due to the adoption of polygon and moving surface mesh, respectively. A convergence study is firstly carried out to verify the consistency. Then, numerical tests of 1-D, 2-D, and 3-D heat conduction problems subject to mixed boundary conditions are performed for verification. Good agreements with theoretical solutions are observed. Natural convection problems with different boundary conditions in an annulus are carried out for further validations of heat-fluid coupling. Excellent agreements between the present and literature results are presented. Finally, problem of heat convection in a square droplet oscillation is demonstrated to show the capability of dealing with moving free surface.