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Report No.

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

Wang, Z.; Duan, G.*; Matsunaga, Takuya*; Sugiyama, Tomoyuki

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 geometries can be easily treated due to the use of polygons for wall boundary. A convergence study was firstly carried out to verify the consistency. Then, numerical tests of 1-D and 2-D heat conduction problems subjected to mixed boundary conditions were performed for verification, and good agreements with theoretical solutions were observed. Natural convection problems with different boundary conditions in an annulus were carried out for further validations of heat-fluid coupling. Excellent agreements between the present and literature results were demonstrated.



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