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We describe a series of computational experiments that employ nonoscillatory finite volume methods to simulate the decay of high Reynolds number turbulence. These experiments cover a broad range of physical viscosities and numerical resolutions. We have extracted a data set from these experiments detailing the energy dissipation by physical viscosity and by the numerical algorithm. We offer a preliminary analysis of this data, including new insights into the (computational) transition between direct numerical simulation and large eddy simulation. [DOI: 10.1115/1.2176749]

Implicit turbulence modeling is the numerical simulation of high Reynolds fluid flow using nonoscillatory finite volume (NFV) schemes without any explicit subgrid scale model. Here we investigate the ability of a particular NFV scheme, MPDATA, to simulate decaying turbulence in a triply periodic cube for a variety of viscosities, comparing our results to analogous pseudo-spectral studies. In the regime of direct numerical simulation, MPDATA is shown to agree closely with the pseudo-spectral results. As viscosity is reduced, the two model results diverge. We study the MPDATA results in the inviscid limit, using a combination of mathematical analysis and computational experiment. We validate these results as representing the turbulent flow in the limit of very high Reynolds number. [DOI: 10.1115/1.1514210]

The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics. This article is part of the theme issue 'Hilbert's sixth problem'. [ABSTRACT FROM AUTHOR]

Considers three different sets of shallow water equations representing different levels of approximation. Comparison of numerical solutions of these different equations for flow past bottom topography in several different flow regimes; Level of approximation required for a particular flow.