This thesis presents and analyzes several meshless numerical methods of solving nonlinear diffusion equation arising from physical modeling of enthalpy transfer during solidification process of an alloy. Spatial derivatives are discretized using radial basis function-generated finite difference (RBF-FD) method. For a time integration scheme the explicit and implicit Euler schemes are used. Additionally, an alternative implicit time scheme is derived and is solved using Newton’s iteration for nonlinear system of equations. We describe two stabilization techniques, namely the oversampled RBF-FD method and the ghost node method. At last, the convergence of different methods with respect to node refinement and their ability of reproducing the temperature–enthalpy relationship are compared.
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