Computational Studies of Convective Transport in Evolving Domains

本程序将开发一种计算算法来计算具有变化边界条件的区域的耦合能量和流体动力学方程，例如在涉及凝固、沉积和溶解的问题中所经历的那些。新算法将尝试结合边界积分法和谱元素法的特点，以达到高精度和高效率，同时保持足够的灵活性来处理变化的几何形状。我们将讨论两种形式：一种是使用Stokes近似并单独使用边界积分方法来处理非常慢的流动，另一种是使用Navier-Stokes方程和边界元-谱元相结合的方法来处理自然对流。随着该项目的成功完成，这些工具将可用于研究不断演变的系统的最一般的对流换热过程。这种能力将使我们更好地理解诸如凝固、溶解、蚀刻和腐蚀等现象。

This program will develop a computational algorithm to calculate the coupled energy and hydrodynamic equations for domains with changing boundary conditions such as those experienced in problems involving solidification, deposition, and dissolution. The new algorithm will attempt to combine the features of the boundary integral method with the spectral element method to achieve high accuracy and efficiency while remaining sufficiently flexible to handle the changing geometries. Two formulations will be treated: One involving very slow flow using the Stokes approximation and employing the boundary integral method alone, and the second involving natural convection using the Navier-Stokes equations and the combined boundary element-spectral element approach. With the successful conclusion of this project, the tools will be available to study the most general convective heat transfer processes for evolving systems. This ability will lead to a better understanding of such phenomena as solidification, dissolution, etching, and corrosion.