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Large-scale simulations are often under-resolved at some level, but they are still useful in extracting both qualitative and quantitative information about the flow. In order to use such results effectively we need to characterize the numerical uncertainty of under-resolved simulations. However, different numerical methods exhibit different behavior, and spectral — based methods in particular may...
Over the past decade there has been an increasing amount of evidence that high resolution numerical methods for hyperbolic partial differential equations have an embedded (or “implicit”) turbulence model. The present chapter describes this general class of methods and outlines the basic structure of high resolution methods as an effective turbulence model in the context of large eddy simulation (LES)...
We propose to perform turbulent flow simulations in such manner that the difference operators do have the same symmetry properties as the corresponding differential operators. That is, the convective operator is represented by a skew-symmetric difference operator and the diffusive operator is approximated by a operators forms in itself a motivation for discretizing them in a certain manner. We give...
Turbulent flows are characterised by a continuum of length and time scales, a feature that introduces some unique problems in relation to the analysis and control of errors in numerical simulations of turbulent flows. In direct numerical simulation (DNS) one attempts to fully resolve the flow field. The primary sources of error in DNS are the aliasing error, which arises due to the evaluation of the...
A general framework for the design of adaptive low-dissipative high order schmes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that...
This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential...
The α-modeling strategy is followed to derive a new subgrid parameterization of the turbulent stress tensor in large-eddy simulation (LES). The LES-α modeling yields an explicitly filtered subgrid parameterization which contains the filtered nonlinear gradient model as well as a model which represents Leray-regularization. The LES-α model is compared with similarity and eddy-viscosity models that...
The Earth’s atmosphere and oceans are essentially incompressible, highly turbulent fluids. Herein, we demonstrate that nonoscillatory forward-in-time (NFT) methods can be efficiently utilized to accurately simulate a broad range of flows in these fluids. NFT methods contrast with the more traditional centered-in-time-and-space approach that underlies the bulk of computational experience in the meteorological...
Direct numerical simulations have recently emerged as a viable tool to understand finite Reynolds number multiphase flows. The approach parallels direct numerical simulations of turbulent flows, but the unsteady motion of a deformable phase boundary add considerable complexity. Here, a method based on solving the Navier-Stokes equations by a finite difference/front tracking technique that allows the...
This chapter is intended to convince the reader, through a number of relevant and diverse examples, that modern CFD with turbulence modelling is a practical tool for fast and accurate prediction of flow problems of engineering interest. A general introduction to modern CFD and a preface to the general-purpose CFD solver, CFD++, are followed by a substantial number of flow examples.
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