Scientific Computation of Physical Problems

将在以下领域进行研究：中子输运理论中的计算和分析问题(C.Borgers)。将研究稀薄气体动力学和中子输运的问题。1)气膜润滑传统上用雷诺方程来描述，该方程是由可压缩的N-S方程导出的。这里提出了一种基于最简单的动力学模型--自由分子流的方法。2)将研究这一语句的离散类比，重点是时间离散化。粘性双曲守恒定律和哈密尔顿-雅各比方程(E.哈拉贝斯蒂安)。这一建议涉及双曲型守恒律及其粘性摄动和Hamilton-Jacobi方程问题的数值技术的分析和发展。提出的具体问题是：1)双曲型守恒律的多维前沿传播和粘性效应的模拟。2)Hamilton-Jacobi方程收敛到定态，并应用于“Shape for Shading”问题。涡旋片计算(R.Krasny)。将对涡片运动的各个方面进行研究。1)将涡团方法推广应用于分流平板流动。2)研究了紧致截断函数和涡片运动的多极算法。3)将涡团、Navier-Stokes和尾流实验结果进行比较，以评估涡片模型中忽略物理粘性的影响。4)在自由空间和圆管边缘计算轴对称涡片卷曲。

The research to be performed will be in the following areas: Computational and Analytical Problems in Neutron Transport Theory (C. Borgers). Problems from rarefied gas dynamics and neutron transport will be studied. 1) Gas film lubrication is traditionally modeled by the Reynolds equation, derived from the compressible Navier-Stokes equations. Here an approach based on the simplest kinetic model, free molecular flow, is proposed. 2) Discrete analogs of this statement will be studied, with emphasis on time discretization. Viscous Systems of Hyperbolic Conservation Laws and Hamilton-Jacobi Equations (E. Harabetian). This proposal concerns the analysis and development of numerical techniques for problems in hyperbolic conservation laws and their viscous perturbation, and Hamilton-Jacobi equations. The specific problems proposed are 1) Multidimensional front propagation for hyperbolic conservation laws and the modeling of viscous effects. 2) Convergence to a steady state for Hamilton-Jacobi equations, with application to "shape for shading" problems. Vortex Sheet Computations (R. Krasny). Various aspects of vortex sheet motion will be studied. 1) The vortex blob method will be extended and applied to splitter plate flow. 2) Compact cutoff functions and multipole algorithms for vortex sheet motion will be investigated. 3) Vortex blob, Navier Stokes, and experimental results for wake flow will be compared, to asses he effect of neglecting physical viscosity in the vortex sheet model. 4) Axisymmetric vortex sheet roll-up will be computed, in free space and at the edge of a round pipe.