Mathematical Sciences: Cartesian Grid Methods for Compressible Flow

数学科学：可压缩流的笛卡尔网格方法

• 批准号: 9204329
• 负责人: Randall LeVeque
• 金额: $ 9万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9204329&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cartesian; Grid; Methods

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.

这项研究涉及到在多个空间维度上发展随时间变化的气体动力学计算的数值方法。其目标是开发基于底层均匀笛卡尔网格的方法，即使在几何形状复杂且所模拟的现象涉及相对于网格具有任意方向的复杂特征时也是如此。具体方面包括对通过笛卡尔网格单元的界面或边界切割产生的不规则单元开发更好的多维有限体积方法，以及将这种方法与激波跟踪和复合网格结合使用。流体流动的计算机模拟对于理解和模拟科学和技术中的各种重要过程至关重要。仅举一个例子，为了确定飞机的飞行情况和设计安全、省油的车辆，需要对飞行中的飞机周围的空气流动进行建模。计算机方法通过近似求解一组复杂的微分方程组，产生飞机周围有限网格点上的空气速度和压力的近似值。需要数百万个网格点才能很好地逼近复杂物体周围的流动，这使得即使是最强大的计算机也达到了极限。这项工作的目标是开发更有效和更准确的方法来解决这类问题，特别是强调更好地处理具有复杂形状的物体(如飞机)和对具有复杂行为的流动进行建模。