Computational Analysis of Fluid Flows: External Boundaries Interior Layers and Nonlinear Waves

本项目涉及随时间流体流动的计算分析，它涉及设计可靠和有效的数值方法来解决无界域上的问题和模拟波在反应介质中的传播。这项工作的一个方面是开发和测试欧拉和纳维-斯托克斯方程的渐近边界条件的外和柱域。主要的工具是对波的长距离传播的渐近分析。该方法的一个优点是精度提高，精度可以通过改变域大小或改进渐近逼近来控制。第二个关注的领域是多维扩散波的存在性、稳定性和动力学的计算研究。一个应用是火焰在通道中传播的模型，包括壁面热损失的影响。本文还将研究奇异摄动问题的数值分析。重点是具有刚性源项的双曲问题和复杂系统的长时间模拟。贯穿全书的统一主题是计算分析和渐近分析之间的相互作用。

This project is concerned with the computational analysis of time dependent fluid flows and it involves both the design of reliable and efficient numerical methods for problems on unbounded domains and the simulation of wave propagation in reactive media. One aspect of this work is the development and testing of asymptotic boundary conditions for the Euler and Navier-Stokes equations in exterior and cylindrical domains. The main tool is the asymptotic analysis of the long range propagation of waves. An advantage of this approach is enhanced accuracy, which may be controlled by varying the domain size or improving the asymptotic approximations. A second area of concentration is the computational study of existence, stability and dynamics of multidimensional diffusive waves. One application is to a model of flame propagation in a channel, including the effects of heat loss at the walls. The numerical analysis of singular perturbation problems will also be studied. The emphasis is on hyperbolic problems with stiff source terms and on the long time simulation of complex systems. The unifying theme throughout is the interplay between computational and asymptotic analysis.