Meshless approach to the large-eddy simulation of the continuous casting process

The paper discusses the numerical solution of the large-eddy formulation for modelling the turbulent fluid flow with solidification in the continuous casting of steel. This industrially relevant problem is solved by a meshless method for the first time. The solid-liquid system is formulated within the continuum mixture formulation of the governing, mass momentum and energy equations. The Darcy porous media model describes the mushy region. The large-eddy formulation is based on the Smagorinsky model for sub-grid scale viscosity and the van Driest damping function. The synthetic turbulence is prescribed at the molten steel inlet. The generated turbulent fluctuations are isotopic and correlated in time through an asymmetric time filter. Explicit time discretisation, combined with meshless local radial basis function collocation method, is employed. Five-noded subdomains, non-uniform node arrangement and multiquadrics shape functions are used for solving a two-dimensional model. The sensitivity to different node arrangements, time steps, inlet temperature, and velocity boundary conditions is elaborated and successfully verified by comparison with our previously published meshless k − ε turbulence model of the same process.