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International audience; The present paper deals with the numerical simulation of a multiphase system. The solidification of a binary alloy in a rectangular domain is considered. Coupled volume averaged governing equations for mass, energy, momentum and species transfer are introduced as a governing system. The phase properties are resolved from the Lever solidification rule, the fluid dynamics in the porous mushy zone is modeled by a Darcy force and the liquid phase is assumed to behave like an incompressible Newtonian fluid. Double diffusive effects in the melt are modeled by the thermosolutal Boussinesq hypothesis. The governing equations are solved by the novel Local Radial Basis Function Collocation Method (LRBFCM). The fields of all physical quantities are represented on overlapping 5-noded sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The equations are solved through explicit temporal discretization and the pressure-velocity coupling is calculated through a local pressure correction scheme. The advantages of the represented meshless approach are its simplicity, accuracy, similar coding in 2D and 3D, and straightforward applicability in nonuniform node arrangements and adaptive node arrangements. The presented spatial discretization technique shows several convenient properties and possibilities for upgrade, whereas stays simple and extremely CPU efficient. On the other hand, the completely local solution procedure makes the implementation and parallelization straightforward (without solving big systems of equations).