A coupled domain–boundary type meshless method for phase-field modelling of dendritic solidification with the fluid flow

Abstract

Purpose This study aims to simulate the dendritic growth in Stokes flow by iteratively coupling a domain and boundary type meshless method. Design/methodology/approach A preconditioned phase-field model for dendritic solidification of a pure supercooled melt is solved by the strong-form space-time adaptive approach based on dynamic quadtree domain decomposition. The domain-type space discretisation relies on monomial augmented polyharmonic splines interpolation. The forward Euler scheme is used for time evolution. The boundary-type meshless method solves the Stokes flow around the dendrite based on the collocation of the moving and fixed flow boundaries with the regularised Stokes flow fundamental solution. Both approaches are iteratively coupled at the moving solid–liquid interface. The solution procedure ensures computationally efficient and accurate calculations. The novel approach is numerically implemented for a 2D case. Findings The solution procedure reflects the advantages of both meshless methods. Domain one is not sensitive to the dendrite orientation and boundary one reduces the dimensionality of the flow field solution. The procedure results agree well with the reference results obtained by the classical numerical methods. Directions for selecting the appropriate free parameters which yield the highest accuracy and computational efficiency are presented. Originality/value A combination of boundary- and domain-type meshless methods is used to simulate dendritic solidification with the influence of fluid flow efficiently.

Assessment of Local Radial Basis Function Collocation Method for Diffusion Problems Structured with Multiquadrics and Polyharmonic Splines

“…where l r 0 is the scaling parameter, and the first-and second-order derivatives of the PHS are given in Equations ( 24)- (27).…”

“…According to [24], the convergence rate of the method using PHSs can be controlled with the highest order of augmentation monomials, meaning the higher the polynomial degree, the better the convergence rate, but it will also require larger subdomains and, as a result, more computation time. Many tests and experiments have recently been performed using PHS, such as the solidification of pure materials, solidification of binary alloys, phase-field modelling of solidification [27], an improved local radial basis function method for solving small-strain elasto-plasticity [28], a hybrid radial basis function finite difference method for modeling two-dimensional thermo-elasto-plasticity [29], and its application to the metallurgical cooling bed problem [30]. An application of PHSs to a real-world problem can be seen in the study of the reduction in discretization-induced anisotropy in the phase-field modeling of dendritic growth via the meshless approach [31].…”

Meshless Interface Tracking for the Simulation of Dendrite Envelope Growth

“…to the smallest internodal distance, therefore the optimal approach would be to scale time-step according to the varying ℎ. In a recent paper [57] authors used quad-tree time step adaptivity to take this into account. In this paper, however, we use a global time step, which we set according to the stability criterion for the smallest internodal distance with additional safety margin.…”

Effect of Forced Convection on Magnesium Dendrite: Comparison between Constant and Altering Flow Fields

“…More than 90 percent of Mg products are manufactured by cast Mg alloys which are formed by smelting and solidification. During this process, the filling condition changes dramatically, which directly affects melt convection and thus evolution of solidification microstructures [5][6][7][8]. Exploring the relationship between the convection and the Mg alloy microstructures can guide optimization of the microstructures and thus improvement of the material properties.…”