We present the Scale Adaptive Dendritic Envelope (SADE) model of solidification at mesoscopic scales. The new approach is based on the rescaling of the microscopic laws on the desired resolution scale of simulation. The diffusivity, the Gibbs Thomson coefficient, and the fraction which solidifies with the solid front are modified to create large fictitious dendrites (envelope) whose tips growth at the same speed as the microscopic tips. The model is inspired from the methodology of the turbulence models that filter the scales that are smaller than the simulation grid size, such as the Large Eddy Simulation (LES) approach. Here, the solidified structure scales which are smaller than the grid size, such as the tip radius and the smallest arms, are modelled with sub-grid scale models. The envelope growth is coupled with a subgridmodel to account for the contribution of the unresolved secondary arms to the phase transformation. The model is applied to constitutionally undercooled domains with different grid sizes that are larger than the initial secondary arm spacing and much larger than the microscopic tip radius. A similar primary arm spacing is predicted regardless of the grid resolution. However the result obtained with smaller meshes resolve more dendrites branches than with coarser meshes.
|Number of pages
|IOP Conference Series: Materials Science and Engineering
|Published - 2015