A large-eddy simulation (LES) based meshless model is developed for the three-dimensional (3D) problem of continuous casting (CC) of steel billet. The local collocation meshless method based on radial basis functions (RBF) is applied in 3D. The method applies scaled multiquadric (MQ) RBF with a shape parameter on seven nodded local sub-domains. The incompressible turbulent fluid flow is described using mass, energy, and momentum conservation equations and the LES turbulence model. The solidification system is solved with the mixture continuum model. The Boussinesq approximation for buoyancy and the Darcy approximation for porous media are used. Chorin’s fractional step method is used to couple velocity and pressure. The microscopic model is closed with the lever rule model. The LES model is compared to the two-equation Low Re $k-\epsilon$ turbulence Reynolds Averaged Navier–Stokes (RANS) model in terms of temperature, velocity and computational times. The LES model resolves transient character of vortices which RANS-type turbulence models are unable to tackle. The computational cost of LES models is considerably higher than in RANS. On the other hand, it results in a much lower computational cost than the direct numerical simulation (DNS). The paper demonstrates the ability of the method to solve realistic industrial 3D examples. Trivial adjustment of nodal densities, high accuracy, and low numerical diffusivity are the main advantages of this meshless method.

Continuous casting is the most widely used process in the steelmaking industry. Understanding the physical phenomena and modeling them is essential for mitigating casting defects. This study uses a mixture-continuum formulation in axisymmetry to model this process computationally. A physical model incorporating coupled mass, momentum, and energy equations for solidification with melt turbulence was employed, assuming Newtonian, incompressible behavior and the k-epsilon turbulence model. The model provides insights into the thermo-fluid dynamics during solidification. For the numerical simulation, the Local Radial Basis Function Collocation Method (LRBFCM), a meshless approach, is utilized and compared against the more traditional Finite Volume Method (FVM). The results demonstrate that the meshless LRBFCM offers comparable accuracy and convergence to the FVM while reducing the computational complexity associated with mesh generation. These findings suggest that LRBFCM is a viable alternative for simulating complex metallurgical processes, such as continuous casting, with competitive performance.