Development, Analysis and Applications for Numerical Methodsfor Nonlinear Partial Differential Equations

Osher、Engquist等教授将继续各自和共同研究非线性偏微分方程数值方法的发展、分析和应用。具体研究方法包括：本质上是非振荡激波捕获技术，前沿捕获算法，多分辨率和基于小波的方法，数值均匀化，有效边界条件，动力学模型，光谱和粘度方法，粒子方法，随机差分法。需要研究的工程和物理应用包括：高速飞行器的空气动力学特性、流体动力学装置模型、多孔介质中的混流、燃烧、反应气体流动、激波湍流相互作用、微波散射、玻尔兹曼方程、核聚变反应堆和堆芯环流。这一范围广泛的活动在其本身和广泛应用方面都具有价值。

Professors Osher, Engquist, and others will continue their individual and joint research on the development analysis and applications of numerical methods for nonlinear partial differential equations. Specific methods to be studied include: essentially nonoscillatory shock capturing techniques, front capturing algorithms, multiresolution and wavelet based methods, numerical homogenization, effective boundary conditions, kinetic models, spectral and viscosity methods, particle methods, and stochastic difference methods. Engineering and physical applications to be studied include: aerodynamical properties of high speed vehicles, hydrodynamic device models, miscible flow in porous media, combustion, reacting gas flows, shock turbulence interactions, microwave scattering, Boltzmann equations, nuclear fusion reactors, and core-annular flows. This broad range of activity has value both in its own right and with regard to extensive applications.