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

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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.