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

该项目涉及的计算分析 与时间相关的流体流动，并且它涉及 可靠和有效的数值方法的问题， 无界区域和模拟波的传播 反应介质 这项工作的一个方面是开发和测试 Euler和Navier-Stokes渐近边界条件 方程的外部和圆柱域。 主要工具是 波的长程传播的渐近分析。 这种方法的优点是提高了准确性，这可能是有利的。 通过改变域的大小或提高渐近 近似值 第二个集中的领域是计算研究 多维扩散方程的存在性、稳定性和动力学 波 一个应用是火焰传播的模型， 通道，包括在墙壁上的热损失的影响。 的 奇异摄动问题的数值分析也将 研究了 重点是双曲型问题， 源项和复杂系统的长时间模拟。 贯穿始终的统一主题是 计算和渐近分析。

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.