Parallel Adaptive Mesh Refinement Algorithm Research Articles

Phase-field lattice-Boltzmann study on dendritic growth of hcp metals under gravity-driven natural convection

A phase-field lattice-Boltzmann method coupled with the parallel-adaptive mesh refinement algorithm is developed to simulate the equiaxed and columnar dendritic growth of hcp metal alloys. The effect of gravity-driven natural convection on the dendritic growth is discussed separately and also coupled with forced convection. The simulated results show the asymmetric dendritic growth of hcp metal alloys in two dimensions under gravity-driven natural convection, and reveal the evolution process of solute segregation and solute plumes. It can be concluded that the solute plume formation is determined by the competition between the solute blocking of dendrites and solute transport of the melt flow. Introducing an appropriate forced convection can eliminate the solute plume formation and dampen the local fluctuation of solute concentration in front of the dendrite tips. It is also found that the gravity-driven natural convection enriches the diversity of the 3D dendritic morphology of hcp metal alloys.

Numerical investigation of eutectic growth dynamics under convection by 3D phase-field method

Control of eutectic growth trajectory is a technologically important subject in metallurgy and applied physics. The interaction between solute transport and interface capillary determines eutectic growth under convection. By employing a multiphase-field lattice-Boltzmann method, together with a parallel-adaptive mesh refinement algorithm, the effect of convection on 3D eutectic growth is quantified including lamellar and rod eutectics. The flow-induced solute distribution changes eutectic growth dynamics by establishing a new solute transport equilibrium. The growth behaviors of different eutectic patterns are investigated, and the eutectic growth dynamics is largely dependent on the constitutional undercooling and the curvature undercooling ahead of the solidification front. The natural convection changes the width ratio of coexisting solid phases, while the forced convection causes a tilt band for both lamellar and rod eutectics. Rod-to-lamellar transition under larger convection intensity, which is first predicted by numerical techniques, is discussed and good agreement with previous works is achieved. The deep understanding of the convection effect can help guide how to regulate eutectic patterns through changing the solidification condition.

Phase-field modeling of dendritic growth of magnesium alloys with a parallel-adaptive mesh refinement algorithm

A two-dimensional phase field (PF) model was developed to simulate the dendritic solidification in magnesium alloy with hcp crystal structure. By applying a parallel-adaptive mesh refinement (Para-AMR) algorithm, the computational efficiency of the numerical model was greatly improved. Based on the PF model, a series of simulation cases were conducted and the results showed that the anisotropy coefficient and coupling coefficient had a great influence on the dendritic morphology of magnesium alloy. The dendritic growth kinetics was determined by the undercooling and equilibrium solute partition coefficient. A significant finding is acquired that with a large undercooling, the maximum solute concentration is located on both sides of the dendrite tip in the liquid, whereas the maximum solute concentration gradient is located right ahead of the dendrite tip in the liquid. The dendrite tip growth velocity decreases with the increase of the equilibrium solute partition coefficient, while the variation trend of the dendrite tip radius is the opposite. Quantitative analysis was carried out relating to the dendritic morphology and growth kinetics, and the simulated results are consistent with the theoretical models proposed in the previously published works.

Phase-field lattice-Boltzmann study on eutectic growth with coupled heat and solute diffusion

The thermosolutal interaction influences eutectic evolution and thus properties of solidified materials. Limited by numerical capability, however, very few studies are performed on the eutectic growth with coupled heat and solute diffusion. Combining the phase-field lattice-Boltzmann approach and a parallel-adaptive mesh refinement algorithm, a novel numerical scheme is developed to efficiently simulate the thermosolutal multiphase eutectic evolution. The contact angles at the triple point agree well with the analytical solution, and the temperature always obtains the local extreme at the solid/liquid interface due to the release of latent heat. The effects of the Lewis number and imposed heat sink on the eutectic evolution are discussed in detail, which includes the change of the lamellar growth velocity and the form of lamellae creation. The dimension is further extended to 3D to investigate the evolution of plate- and rod-like eutectics. How to simulate eutectic evolution with a larger Lewis number (e.g., 106) and how to develop a more general eutectic model are also discussed. As the first attempt to solve the thermosolutal eutectic evolution, our investigation paves a way for further quantitative analysis and direct comparison with experiments.

Three-dimensional numerical simulation of bubble rising in viscous liquids: A conservative phase-field lattice-Boltzmann study

Simulating bubble rising in viscous liquids is challenging because of the large liquid-to-gas density ratio and complex topological evolution of the gas-liquid interface. In this study, a conservative phase-field model is employed to accurately track the interface during bubble rising, and the lattice Boltzmann model is used to determine the flow field driven by the buoyancy force and the surface tension force. To facilitate large-scale three-dimensional simulations, a parallel-adaptive mesh refinement algorithm is developed to reduce the computing overhead. The simulated bubble shapes under different configurations are compared with the shape chart through experiments [D. Bhaga and M. E. Weber, “Bubbles in viscous liquids: shapes, wakes, and velocities,” J. Fluid Mech. 105, 61–85 (1981)]. The influence of the numerical parameters (including domain size, surface tension, liquid viscosity, gravity, and density ratio) on the bubble dynamics is investigated, which demonstrates the capability of the current numerical scheme in simulating multiphase flow. Furthermore, complex topology changes including the bubble coalescence, splitting, and interplay with obstacles (i.e., squeeze deformation and bubble splitting) are simulated and compared in different cases, i.e., with different Reynolds, Eötvös, and Morton numbers. The effect of the initial bubble spacing on the coalescence of the two bubbles and the influence of boundary conditions on multiple bubble dynamics are investigated. When the bubbles can be completely blocked by the obstacle is quantified in terms of the obstacle width. Numerical results validate the robustness of the present numerical scheme in simulating multiphase flow.

A parallel adaptive viscoelastic flow solver with template based dynamic mesh refinement

A parallel adaptive mesh refinement algorithm has been incorporated into the side-centered finite volume method [Sahin, A stable unstructured finite volume method for parallel large-scale viscoelastic fluid flow calculations. J. Non-Newtonian Fluid Mech., 166 (2011) 779–791] in order to obtain highly accurate numerical results for viscoelastic fluid flow problems. The present recursive mesh refinement algorithm is based on a conformal refinement of unstructured quadrilateral/hexahedral elements with templates based on 1:3 refinement of edges. In order to transfer cell-centered data between source and target meshes, a second-order conservative interpolation (remapping) technique similar to the work of Menon and Schmidt [Supermesh construction for conservative interpolation on unstructured meshes: An extension to cell–centered finite-volume variables. Comput. Methods Appl. Mech. Eng., 200 (2011), 2797–2804] are employed and the approach has been extended for side-centered data. The proposed framework has been applied to the classical benchmark problem of an Oldroyd-B fluid past a confined circular cylinder in a rectangular channel and a sphere falling in a circular tube. The calculations confirm that high accuracy can be achieved with the present adaptive mesh refinement.

A parallel adaptive mesh refinement algorithm for predicting turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed for predicting turbulent non-premixed combusting flows characteristic of gas turbine engine combustors. The Favre-averaged Navier–Stokes equations governing mixture and species transport for a reactive mixture of thermally perfect gases in two dimensions, the two transport equations of the k–ω turbulence model, and the time-averaged species transport equations, are all solved using a fully coupled finite-volume formulation. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. This AMR approach allows for anisotropic mesh refinement and the block-based data structure readily permits efficient and scalable implementations of the algorithm on multi-processor architectures. Numerical results for turbulent non-premixed diffusion flames for a bluff-body burner are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting complex non-premixed turbulent combusting flows.