ALGORITHMS: Parallel Level Set Method on Adaptive Cartesian Grids for Multi-Scale Interfacial Flow Computation

自然界中许多物理现象都涉及分隔两个或多个区域的界面的运动。水平集方法是一种基于pde的方法，旨在通过有符号距离函数的演化来捕获界面运动。本探索性项目旨在进一步将水平集方法扩展到非结构化自适应笛卡尔网格。我们计划解决以下研究任务：开发支持自适应笛卡尔网格和各种数据结构的水平集求解器，包括树和基于列表的数据结构。该求解器将与基于界面的自适应笛卡尔网格适配器耦合，以提高界面分辨率并减小界面附近的数值误差。将开发并提供一套软件工具，用于训练学生掌握基本的界面动力学，并在具有挑战性的工程和科学学科中进行研究。

Numerous physical phenomena in nature involve the motion of interfaces separating two or more regions. The level-set method was a PDE-based approach designed to capture the interface motion through the evolution of a signed distance function. This exploratory project aims to further extend the level-set method to unstructured adaptive Cartesian grids. We plan to address the following research task: Development of a level-set solver supporting the adaptive Cartesian grids, and various data structures including both tree and list-based data structures. This solver will be coupled to an adaptive Cartesian grid adaptor for interface based grid adaptations to improve the interface resolution and decrease the numerical errors near the interface.A set of software tools will be developed and made available that can be used to both train students with basic interface dynamics, and to conduct research in challenging engineering and scientific disciplines.