Abstract
This study is aimed at establishing an effective incremental-iterative framework, for the first time, using reproducing kernel collocation method for solving multi-phase dynamic coupling problems in a porous enclosure. The central difference method is utilized in the temporal discretization while direct collocation with reproducing kernel approximation is adopted in the spatial discretization, in particular, with Newton–Raphson method for nonlinear iteration. Under the proposed numerical framework, a determined and well-conditioned nonlinear system is ensured during nonlinear iteration. In addition to the traditional mesh-based weak-form methods, it is shown that the present study provides an alternative effective approach to solve unsteady-state double-diffusive convection problems.
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