论文标题
对于3D相固体模型的非结构化网格上有限体积方法的收敛
Convergence of the Finite Volume Method on Unstructured Meshes for a 3D Phase Field Model of Solidification
论文作者
论文摘要
我们提出了适用于适用于模拟纯物质固化的特定相处问题的有限体积方法的收敛结果。该模型由热方程和相位场方程组成，其反应项的一般形式涵盖了各种管理树突生长和基本接口跟踪问题的现有模型。我们将众所周知的紧凑型嵌入技术在有限体积方法的背景下应用于可允许的非结构化多面部网格。我们开发了必要的插值理论，并得出了先验估计，以获得关键术语的界限。基于此估计，我们结论了方程式系统中所有术语的收敛性。
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.
