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Special Applied Math Seminar
Multiscale Analysis and Computation for the 3D Incompressible
Navier-Stokes Equations
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Developing a systematic and reliable turbulence model would have a tremendous impact in many engineering applications. So far, most of the existing turbulence models are based on some closure assumption and contain unknown parameters. Traditional multiscale analysis cannot handle problems with non-separated scales. In this talk, we will present a systematic multiscale analysis for the incompressible Navier-Stokes equation with infinitely many non-separated scales and apply this multiscale analysis to develop an effective multiscale model for turbulent flows. There are two key ingredients in our multiscale analysis. The first one is to reformulate the solution in the Fourier space into a formal two-scale structure. The second one is to introduce a multiscale phase function and a nested multiscale expansion to characterize the propagation of the small scales. Numerical experiments will be presented to demonstrate that the multiscale computational method indeed captures the correct large scale solution of the incompressible Navier-Stokes equations both in two and three space dimensions. |