arXiv subjects

Pavel Strachota

Publications and source records attributed to Pavel Strachota.

4 recordsLinked to original sources

arXiv2024

Three-dimensional phase-field simulations of water freezing and thawing at pore-scale

This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition modeling is approached at both macro-scale and micro-scale, combining heat transfer in a heterogeneous medium and a phase-field approximation of the Gibbs-Thomson relation by means of the Allen-Cahn equation. The formulation of the model contains novel components tailored for the given purpose. At the macro-scale, surface tension effects are negligible and phase transition focusing based on temperature can replace the Allen-Cahn equation. In contrast to that, simulations of equilibrium states at the micro-scale allow to eliminate the heat equation by assuming constant supercooling. For numerical solution, an efficient hybrid parallel algorithm based on the finite volume method and the Runge-Kutta-Merson solver with adaptive time stepping are employed. The results of different model variants at different scales are discussed. In a parametric study, the full phase-field model is demonstrated to deliver consistent results across a wide range of surface tension values, exhibiting curvature-induced premelting if surface tension is artificially exaggerated. As surface tension tends to the realistic values, the results of the phase-field approach those of the simplifed temperature-driven phase transition model. In addition, micro-scale simulations of water freezing at different supercooling values aim to predict the unfrozen water content and compare the results with data from literature. Numerical stability, accuracy, and computational costs are also discussed.

physics.comp-ph↗

arXiv2022

Numerical Optimization of the Dirichlet Boundary Condition in the Phase Field Model with an Application to Pure Substance Solidification

As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition control for the phase field model describing the solidification of a pure substance from a supercooled melt. In particular, our aim is to control the time evolution of the temperature field on the boundary of the computational domain in order to achieve the prescribed shape of the crystal at the given time. To obtain efficient means of computing the gradient of the cost functional, we derive the adjoint problem formally. The gradient is then used to perform gradient descent. The viability of the proposed optimization method is supported by several numerical experiments performed in one and two spatial dimensions. Among other things, these experiments show that a linear reaction term in the phase field equation proves to be insufficient in certain scenarios and so an alternative reaction term is considered to improve the models behavior.

math.OC↗

arXiv2020

Convergence of the Finite Volume Method on Unstructured Meshes for a 3D Phase Field Model of Solidification

We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a general form of the reaction term which encompasses a variety of existing models governing dendrite growth and elementary interface tracking problems. We apply the well known compact embedding techniques in the context of the finite volume method on admissible unstructured polyhedral meshes. We develop the necessary interpolation theory and derive an a priori estimate to obtain boundedness of the key terms. Based on this estimate, we conclude the convergence of all of the terms in the equation system.

math.NA↗

arXiv2020

Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of latent heat release during solidification. In this context, several existing forms of the reaction term are analyzed. Inspired by the known conclusions of matched asymptotic analysis, we propose new variants that are simple enough to allow mathematical and numerical analysis and robust enough to be applicable to solidification under very large supercooling. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence and model parameter settings. Despite the phase interface thickness being relatively large to make numerical computations feasible, the obtained results exhibit a good quantitative agreement with experimental data from rapid solidification of nickel melts.

physics.comp-ph↗