Simulation of macrosegregation benchmark on a non-uniform computational node arrangement with a meshless method

An application of a meshless numerical method on a macrosegregation benchmark case is developed in the present paper. The test case is solidification in 2D rectangular cavity, filled with liquid metal and chilled from both sides. This is a highly non-linear problem due to a strong coupling of the macroscopic transport equations with the microsegregation model. The main result is the macrosegregation pattern of the solidified metal Al4.5wt%Cu alloy is used for evaluation of the problem. The model uses diffuse approximate meshless method with the second-order polynomial basis for spatial integration and explicit time-stepping. Simulations are performed on uniform and non-uniform computational node arrangements and compared to each other. The results on uniform and non-uniform node arrangements show a very good matching with the finite volume method results and results based on radial basis function collocation method. This shows that diffuse approximate method based on non-uniform node arrangements can be used for solving macrosegregation problems

Simulation of macrosegregation in low-frequency electromagnetic casting by a meshless method

The novel use of a meshless numerical approach for simulation of macrosegregation in the low-frequency electromagnetic casting is presented along with the analysis of the simulation results. The casting model includes a coupled set of mass, momentum, energy, and species conservation equations. Lorentz force is computed with the induction equation and used in the solidification model. The coupled physical model is solved in cylindrical coordinate system and can be used to model aluminium alloy billet production. Explicit scheme is used for the temporal discretization, while the meshless diffuse approximate method is used for the spatial discretization. The method is localized with subdomains containing 14 local nodes. The Gaussian weight is used in the weighted least squares minimization. Furthermore, the Gaussian is shifted upstream, when an upwind effect is required in order to increase the convection stability. Direct chill casting under the influence of electromagnetic field (EMF) is simulated for various electric amplitudes and currents. The material properties of Al-5.25wt%Cu are used. The casting parameters and material properties are constant in all presented simulations, while EMF is turned off in some cases in order to study its effect on solidification. The results show that EMF has a large effect on the melt-flow and solidification. Oscillatory, instead of a steadystate, solution is obtained in case of certain geometries in EMF casting. The effect of EMF is hard to predict without the use of numerical simulations, due to strong coupled effects of casting geometry, casting parameters, and EMF parameters. This shows the need for numerical modelling of this strongly coupled problem for its better understanding

Simulation of macrosegregation benchmark on a non-uniform computational node arrangement with a meshless method

An application of a meshless numerical method on a macrosegregation benchmark case is developed in the present paper. The test case is solidification in 2D rectangular cavity, filled with liquid metal and chilled from both sides. This is a highly non-linear problem due to a strong coupling of the macroscopic transport equations with the microsegregation model. The main result is the macrosegregation pattern of the solidified metal Al4.5wt%Cu alloy is used for evaluation of the problem. The model uses diffuse approximate meshless method with the second-order polynomial basis for spatial integration and explicit time-stepping. Simulations are performed on uniform and non-uniform computational node arrangements and compared to each other. The results on uniform and non-uniform node arrangements show a very good matching with the finite volume method results and results based on radial basis function collocation method. This shows that diffuse approximate method based on non-uniform node arrangements can be used for solving macrosegregation problems