General hierarchical structure to solve transport phenomena with dissimilar time scales: Application in large-scale three-dimensional thermosolutal phase-field problems.

A general hierarchical structure is developed for phase-field lattice-Boltzmann simulations with dissimilar time scales. The number of the grid levels can be artificially selected in a reasonable range, which can enhance the time marching step by two to three orders of magnitude in comparison with explicit methods. Constructed on a massively parallel platform, the mesh distribution is dynamically adjusted according to a gradient criterion. The developed high performance computing scheme is applied to simulate the coupled thermosolutal dendrite evolution. Numerical tests indicate that the computing efficiency can be further improved by two to three orders of magnitude, which makes numerical simulation of fully coupled thermosolutal dendrite growth viable for alloys with Lewis number ∼10^{4}. The domain size which equivalently consists of billions of uniform meshes is handled to simulate multidendrite evolution. Results show that the domain temperature becomes extremely uneven due to the release of latent heat, which causes a significant difference from isothermal solidification. A simple analytical model is proposed to predict the relation between growth velocity and Lewis number, and the growth morphologies of both equiaxed and directional multiple dendrites are discussed. The combination of the hierarchical mesh structure and the phase-field lattice-Boltzmann method provides an efficiency-driven approach to solve the coupled thermosolutal microstructure evolution.