SUMMARYNonlinear characteristic boundary conditions based on nonlinear multidimensional characteristics are proposed for 2-and 3-D compressible Navier-Stokes equations with/without scalar transport equations. This approach is consistent with the flow physics and transport properties. Based on the theory of characteristics, which is a rigorous mathematical technique, multidimensional flows can be decomposed into acoustic, entropy, and vorticity waves. Nonreflecting boundary conditions are derived by setting corresponding characteristic variables of incoming waves to zero and by partially damping the source terms of the incoming acoustic waves. In order to obtain the resulting optimal damping coefficient, analysis is performed for problems of pure acoustic plane wave propagation and arbitrary flows. The proposed boundary conditions are tested on two benchmark problems: cylindrical acoustic wave propagation and the wake flow behind a cylinder with strong periodic vortex convected out of the computational domain. This new approach substantially minimizes the spurious wave reflections of pressure, density, temperature, and velocity as well as vorticity from the artificial boundaries, where strong multidimensional flow effects exist. The numerical simulations yield accurate results, confirm the optimal damping coefficient obtained from analysis, and verify that the method substantially improves the 1-D characteristics-based nonreflecting boundary conditions for complex multidimensional flows.
One of the most practically important problems of computational aero-acoustics is the efficient and accurate calculation of flows around solid obstacles of arbitrary shapes. To simulate flows in complex domains, we combine two mathematical approaches, the Adaptive Wavelet Collocation Method, which tackles the problem of efficiently resolving localized flow structures, and the Brinkman Penalization Method, which addresses the problems of efficiently implementing arbitrary complex solid boundaries. This hybrid approach is applied to unsteady RANS simulations of compressible flows around bluff bodies. The preliminary results of URANS simulations are compared with the recent experimental and numerical results.
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