Professor Oleg Vasilyev

Department of Mechanical Engineering, University of Colorado, Boulder, USA

Lecture: "Adaptive wavelet paradigm for multiscale modeling and simulation in fluid mechanics"


        Wavelet methods in Computational Fluid Dynamics is a relatively young area of research.  Despite their short decade-long existence, a substantial number of wavelet techniques have been developed for numerical simulations of compressible and incompressible Euler and Navier-Stokes equations for both inert and reactive flows. What distinguishes wavelet methods from traditional approaches is their ability to unambiguously identify and isolate localized dynamically dominant flow structures such as shocks, flame fronts or vortices and to track these structures on adaptive computational meshes. In addition, wavelet multiresolution analysis offers a novel paradigm for modeling and simulation of turbulent flows, namely the tight integration of the numerics and physics-based modeling that enables the development of a unified hierarchy of turbulence models of different fidelity. The centerpiece of these models are the energetic coherent structures that capture the dynamics of the flow across the full spectral range. The integration of turbulence modeling with adaptive wavelet methods results in a hierarchical approach, where all or most energetic parts of coherent eddies are dynamically resolved on self-adaptive computational grids, while modeling the effect of the unresolved incoherent or less energetic modes. This talk will consist of three parts. The first part will provide a general overview of wavelet methods for solution of partial differential equations. The second part will focus on different numerical wavelet-based approaches for solving the Navier—Stokes and Euler equations in adaptive wavelet bases as well as provide the background how to use wavelet-based methods for flows in complex geometries. In the last part of the talk the state-of-the-art adaptive multiresolution wavelet methodologies for modeling and simulation of turbulent flows will be discussed.