Finite-scale equations for compressible fluid flow

Abstract

Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier-Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volumeaveraged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier-Stokes equations.

Advances and challenges of applied large-eddy simulation

“…-Aerodynamics, aeroacoustics and compressible flows [5,6]; aspects of external aerodynamics of trains and cars [10]. -Combustion and reacting flows [13].…”

“…Sci., entitled ''Applied large-eddy simulation", has been published in 2009. It comprises 16 articles (primarily review articles with some new contributions) from leading LES specialists and practitioners, and dealing with a broad variety of topics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. The objective of this article is to briefly review this special issue and to further discuss the advances and challenges of LES applied in industrial applications.…”

Peakompactons: Peaked compact nonlinear waves

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“…Volume integrals in the FV representation naturally link with the discrete spatial filtering operation in LES-the socalled top-hat filtering. FVs and MEA have been also crucial ingredients in the analysis connecting ILES with the solution of finite scale NS equations for laboratory observables [12][13][14].…”