Sharp-interface simulation of dendritic growth with convection: benchmarks

We present and validate a numerical technique for computing dendritic growth of crystals from pure melts in the presence of forced convection. The Navier–Stokes equations are solved on a fixed Cartesian mesh and a mixed Eulerian–Lagrangian framework is used to treat the immersed phase boundary as a sharp solid–fluid interface. A conservative finite-volume discretization is employed which allows the boundary conditions to be applied exactly at the moving surface. Results are presented for a range of the growth parameters, namely crystalline anisotropy, flow Reynolds number and Prandtl number. Direct comparisons are made between the present results and those obtained with phase-field methods and excellent agreement is obtained. Values for the tip characteristics are tabulated to serve as benchmarks for computations of two-dimensional dendritic growth with convection.