This paper demonstrates the development of meshless Local Radial Basis Function Collocation Method (LRBFCM) for solution of three dimensional (3D) turbulent molten steel flow and solidification under the influence of electromagnetic stirring (EMS) and its application to continuous casting process of steel billets. A mixture continuum approach is used to formulate the coupled set of macroscopic equations for mass, momentum, energy, turbulent kinetic energy, and dissipation rate in Cartesian coordinates. The mushy zone is treated as a Darcy porous media. The explicit Chorin fractional step method is used to resolve the pressure-velocity coupling. The LRBFCM uses explicit time discretization and spatial discretization with shape-adaptive multiquadrics radial basis functions collocation on non-uniform seven-noded influence domains, and displacement-adaptive upwind scheme. The Lorentz force due to EMS is provided by a one-way coupling by Elmer software. The advantages of the meshless method are trivial adaptation of the nodal densities, simple upgrade to 3D from previous two-dimensional models, and high accuracy. A study on the influence of changing the EMS parameters on the calculated temperature and velocity fields is performed. The paper confirms the ability of LRBFCM meshless solution of a realistic 3D multiphysics industrial problem with complicated swirling flow pattern.
COBISS.SI-ID: 1474474
A numerical procedure is developed to assess and reduce the orientation dependence of the solution to the phase-field model for dendritic growth. The meshless radial basis function-generated finite difference (RBF-FD) method and the forward Euler scheme are used for the spatial and temporal discretisation of the phase-field equations, respectively. A second-order accurate RBF-FD method is ensured by the use of augmentation with monomials up to the second order, while shape-parameter-free polyharmonic splines of the fifth-order are used as the radial basis functions. The performance of the RBF-FD method is assessed on regular and scattered node distributions by observing the mean phase field, the size of the primary dendrite arm, and the growth velocity. The observables at different orientation angles are compared to assess the orientation dependence of the solution. We show for the first time that the use of the RBF-FD method on a scattered node distribution provides a robust approach for the solution of the phase-field model for dendritic solidification with respect to an arbitrary preferential growth direction.
COBISS.SI-ID: 1527466