Mathematical Sciences: Cartesian Grid Methods for Compressible Flow

这项研究涉及数值方法的发展 用于多个时间依赖的气体动力学计算 空间维度我们的目标是开发基于以下内容的方法： 一个基本的均匀笛卡尔网格，即使几何形状是 复杂的，被建模的现象涉及复杂的 具有相对于栅格的任意方向的要素。 具体方面包括发展更好的多- 三维有限体积法 穿过笛卡尔网格单元的界面或边界， 以及结合冲击跟踪使用这种方法 和复合网格。 流体流动的计算机模拟在 理解和建模各种重要的过程 在科学和技术方面。举一个例子， 飞行中的飞机周围需要空气， 确定它的飞行性能，并设计出安全和节能的 车辆.计算机方法产生近似速度 和周围有限网格点处的空气压力 飞机，通过近似求解一组复杂的 微分方程需要数百万个网格点， 获得一个很好的近似的流动周围的复杂的 对象，即使是最强大的计算机， 限制.这项工作的目标是开发更有效和 准确的方法来解决这些问题，特别强调 更好的方法来处理具有复杂形状的物体（例如 飞机）和模拟具有复杂行为的流动。

This research involves the development of numerical methods for time-dependent gas dynamics calculations in more than one space dimension. The goal is to develop methods that are based on an underlying uniform Cartesian grid even when the geometry is complicated and the phenomena being modeled involves complex features with arbitrary orientation relative to the grid. Specific aspects include the development of better multi- dimensional finite volume methods on irregular cells generated by an interface or boundary cutting through a Cartesian grid cell, and the use of such methods in conjunction with shock tracking and composite grids. Computer simulation of fluid flow is critical in understanding and modeling a wide variety of important processes in science and technology. As just one example, modeling the flow of air around an aircraft in flight is required in order to determine how well it flies and to design safe and fuel-efficient vehicles. Computer methods produce approximations to the velocity and pressure of the air at a finite set of grid points around the aircraft, by approximately solving a complicated set of differential equations. Millions of grid points are required to obtain a good approximation to the flow around a complicated object, stretching even the most powerful computers to their limits. The goal of this work is to develop more efficient and accurate methods to solve such problems, with particular emphasis on better ways to handle objects with complicated shapes (such as aircraft) and to model flows with complicated behavior.