A unified modeling paradigm for turbulence, shock waves and boundary layers in computational compressible aerodynamics
Mechanics
Final Report Abstract
Highly accurate computer simulations of complex flows demand methods for the reliable modeling of turbulence as well as sharp layers in the form of shock waves, boundary layers, and multi-fluid interfaces. Existing modeling approaches achieve good results when simulating every single phenomenon on its own, but they interact with each other in an undesirable manner when turbulence and sharp layers occur together. For example, numerical methods based on artificial viscosity for treating shock waves often influence the turbulence model in such a way that the simulation result becomes nonphysical. In this project we have laid down the base of a unified computational modeling framework for complex flows. A key component of this framework that resolves the unwanted interaction is the development of a highly localized approximation approach of sharp layers. This novel strategy eliminates the nonphysical oscillations that typically occur in the approximation of sharp layers. It is general in the sense that it is independent of the underlying mathematical model, however naturally recovers an entropy structure in the context of conservation laws. The approach is then integrated into the variational multiscale method, which constitutes a promising tool for the simulation of turbulent compressible flows, in which practical mesh widths cannot resolve sharp layers as well as tiny turbulent eddies. In the context of multifluid interfaces we have developed a unified framework of the many multi-fluid flow Navier-Stokes Cahn-Hilliard (NSCH) models that appeared in the literature. The novel framework brings all these diffuse-interface NSCH models together, and identifies that there exists just a single NSCH model that is invariant to the choice of variables. Challenging three-dimensional simulations with the novel NSCH model, such as rising bubbles and the contraction of liquid filaments, show excellent agreement with experimental data.
Publications
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A unified framework for Navier–Stokes Cahn–Hilliard models with non-matching densities. Mathematical Models and Methods in Applied Sciences, 33(01), 175-221.
ten Eikelder, M. F. P.; van der Zee, K. G.; Akkerman, I. & Schillinger, D.
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Constraints for eliminating the Gibbs phenomenon in finite element approximation spaces. Mathematical Models and Methods in Applied Sciences, 34(02), 345-384.
ten Eikelder Marco, F. P.; Stoter, Stein K. F.; Bazilevs, Yuri & Schillinger, Dominik
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Space–time computations of exactly time-periodic flows past hydrofoils. Computers & Fluids, 277, 106286.
Lotz, Jacob E.; ten Eikelder Marco, F.P. & Akkerman, Ido
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Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids. Journal of Fluid Mechanics, 990.
ten Eikelder Marco, F.P.; van der Zee Kristoffer, G. & Schillinger, Dominik
