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

这一为期三年的奖项支持加州大学洛杉矶分校的Russel Caflisch、Bjorn Engquist和Stanley Osher、阿奎拉大学的Giovanni Russo以及意大利罗马大学的Maurizio Falcon在流体模拟和控制的分析和数值方法方面的美意合作研究。他们的研究将集中在五个主题上--奇点形成，捕捉多值解和计算不稳定前沿的水平集方法，数值齐次化，泡状流，以及哈密顿-雅可比方程和控制应用的近似格式。这两个研究小组在科学计算、流体力学和偏微分方程式方面拥有互补的专业知识。加州大学洛杉矶分校开发的水平集和冲击捕捉方法将被推广并应用于罗马制定的控制问题。在L的阿奎拉发展的粒子方法将应用于涡流寻找奇点和验证水平集方法。L的阿奎拉小组在粒子方法研究方面的资历将有助于将加州大学洛杉矶分校守恒定律小组的专业知识整合到现行的CFD程序中。这两个小组的合作应该会扩大对流体动力学中几类重要问题的理解和数值方法。

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.