Acceleration of Macrosegregation Simulation Based on Lattice Boltzmann Method

Abstract

Lattice Boltzmann Method (LBM), newly developing technique of computational fluid dynamics, is coupled with solute and energy conservation equations to develop a macrosegregation simulation model (LBM-coupled model) with high computational efficiency. LBM does not require time-consuming calculations for correction of velocity and pressure of fluid in contrast to methods directly solving Navier-Stokes (NS) equation and, therefore, LBM is computationally efficient. In this study, the accuracy of the LBMcoupled model is investigated by calculating the steady state flows and by comparing the results with those of analytical solutions and a conventional model based on the NS equation. The results between them are almost identical with each other and it indicates that the accuracy of the LBM-coupled model is sufficiently high. Moreover, a macrosegregation simulation is carried out for a simple case where the macrosegregation emerges only by natural convection, by means of the LBM-coupled and conventional models. The LBM-coupled model yields almost the same result with the one of NS-based model. Importantly, however, the simulation of LBM-coupled model is about five times faster than the one of NS-based model.

Macrosegregation simulation model based on Lattice-Boltzmann method with high computational efficiency

“…This is the LBM-coupled model developed in the previous work [15]. This model is consistent with Eqs.…”

“…To realize fast computation of macrosegregation simulation, we developed a numerical model by coupling solute and energy conservation equations with Lattice-Boltzmann Method (LBM). The previous LBM-coupled model [15] cannot be applied to metallic alloy systems because of low numerical stability. This problem was resolved in this study to employ modified lattice Bhadnager-Gross-Krook method [16].…”

“…the LBM-coupled model developed in the previous study cannot be applied to real metallic alloy systems. In this model, the numerical stabilities of LBM and the energy conservation equation limit the Prandtl number to about one order of magnitude larger than typical values in metallic alloys [15]. In other words, when the typical value of thermal diffusivity is employed, the viscosity must be one order of magnitude higher than the typical value in metallic alloys in the light of the numerical stability of LBM.…”

“…Importantly, LBM does not require the time-consuming calculation for correction of the velocity and pressure and, hence, it generally enables fast computation of fluid dynamics. Recently, we developed a model for simulating macrosegregation based on LBM in which the NS equation is replaced by the lattice-Boltzmann equation including effects of the thermossolutal flow and Darcy's flow [15]. The accuracy of the LBM-coupled model was investigated by comparing the calculated results for the steady-state flows with the results obtained by analytical solutions and a conventional model based on the NS equation (NS-based model).…”

“…The LBM-coupled model yields almost the same result as the NS-based model. Importantly, the simulation of LBM-coupled model is about five times faster than the one of NS-based model [15].…”