U.S.-Italy Cooperative Research: Numerical and Analytical Methods for Simulation and Control of Fluids

这个为期三年的奖项支持美国-意大利：洛杉矶加州大学的Russel Caflisch、Bjorn Engquist和Stanley Osher与阿奎拉大学的Giovanni Russo和意大利罗马大学“La Sapienza”的Maurizio Falcone合作研究流体模拟和控制的分析和数值方法。 他们的研究将集中在五个主题-奇点形成，水平集方法捕获多值解和计算不稳定的前沿，数值均匀化，泡状流，和近似方案的汉密尔顿-雅可比方程和控制应用。 这两个研究小组在科学计算、流体力学和偏微分方程方面拥有互补的专业知识。 在加州大学洛杉矶分校开发的水平集和冲击捕获方法将被扩展和应用于控制问题，制定在罗马。 在拉奎拉开发的粒子方法将被应用到涡流，寻找奇点和水平集方法的验证。 拉奎拉小组在粒子方法研究方面的资质将有助于将UCLA小组在守恒定律方面的专业知识整合到现行的CFD代码中。 这两个小组的合作应导致扩大的理解和数值方法在几个重要类别的问题在流体动力学。

This three-year award supports U.S.-Italy cooperative research between Russel Caflisch, Bjorn Engquist, and Stanley Osher of the University of California at Los Angeles and Giovanni Russo at the University of Aquila, and Maurizio Falcone, University of Rome, `La Sapienza,` in Italy, on analytical and numerical methods for simulation and control of fluids. Their research will focus on five topics -- singularity formation, level set methods for capturing multivalued solutions and for computing unstable fronts, numerical homogenization, bubbly flow, and approximation schemes for Hamilton-Jacobi equations and control applications. The two research groups possess complementary areas of expertise in scientific computation, fluid mechanics, and partial differential equations. The level set and shock capturing methods developed at UCLA will be extended and applied to control problems as formulated in Rome. Particle methods developed in L'Aquila will be applied to vortical flows to look for singularities and validation of the level set method. The credentials of the L'Aquila group in the study of particle methods will contribute to the integration of the expertise of the UCLA group on conservation laws into active CFD codes. The cooperation of these two groups should lead to an expansion of the understanding and the numerical methodology in several important classes of problems in fluid dynamics.