Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow
10 Jun 1998-Journal of Computational Physics (Academic Press Professional, Inc.)-Vol. 143, Iss: 1, pp 90-124
TL;DR: In this paper, the conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations, and finite difference schemes for regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out.
About: This article is published in Journal of Computational Physics.The article was published on 1998-06-10. It has received 978 citations till now. The article focuses on the topics: Finite difference & Incompressible flow.
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University of Graz1, National Center for Atmospheric Research2, Lawrence Berkeley National Laboratory3, Centre national de la recherche scientifique4, ETH Zurich5, University of Bonn6, University of Giessen7, University of Trier8, Katholieke Universiteit Leuven9, Pacific Northwest National Laboratory10
TL;DR: This study aims to provide a common basis for CPM climate simulations by giving a holistic review of the topic, and presents the consolidated outcome of studies that addressed the added value of CPMClimate simulations compared to LSMs.
Abstract: Regional climate modeling using convection-permitting models (CPMs; horizontal grid spacing 10 km). CPMs no longer rely on convection parameterization schemes, which had been identified as a major source of errors and uncertainties in LSMs. Moreover, CPMs allow for a more accurate representation of surface and orography fields. The drawback of CPMs is the high demand on computational resources. For this reason, first CPM climate simulations only appeared a decade ago. In this study, we aim to provide a common basis for CPM climate simulations by giving a holistic review of the topic. The most important components in CPMs such as physical parameterizations and dynamical formulations are discussed critically. An overview of weaknesses and an outlook on required future developments is provided. Most importantly, this review presents the consolidated outcome of studies that addressed the added value of CPM climate simulations compared to LSMs. Improvements are evident mostly for climate statistics related to deep convection, mountainous regions, or extreme events. The climate change signals of CPM simulations suggest an increase in flash floods, changes in hail storm characteristics, and reductions in the snowpack over mountains. In conclusion, CPMs are a very promising tool for future climate research. However, coordinated modeling programs are crucially needed to advance parameterizations of unresolved physics and to assess the full potential of CPMs.
833 citations
01 Jan 2001
TL;DR: This guide provides the theoretical basis for the Fire Dynamics Simulator (FDS) and a summary of the work performed to evaluate the model, and a survey of work conducted to date to evaluate FDS.
Abstract: Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. Preface The use of fire models currently extends beyond the fire research laboratories and into the engineering, fire service and legal communities. Surveys [1, 2] of available fire models show a significant increase in number over the last decade. Sufficient evaluation of any model is necessary to ensure that users can judge the adequacy of its technical basis, appropriateness of its use, and confidence level of its predictions. This document provides the theoretical basis for the Fire Dynamics Simulator (FDS) and a summary of the work performed to evaluate the model. This guide is based in part on the " Standard Guide for Evaluating the Predictive Capability of De-terministic Fire Models, " ASTM E 1355 [3]. ASTM E 1355 defines model evaluation as " the process of quantifying the accuracy of chosen results from a model when applied for a specific use. " The model evaluation process consists of two main components: verification and validation. Verification is a process to check the correctness of the solution of the governing equations. Verification does not imply that the governing equations are appropriate; only that the equations are being solved correctly. Validation is a process to determine the appropriateness of the governing equations as a mathematical model of the physical phenomena of interest. Typically, validation involves comparing model results with experimental measurement. Differences that cannot be explained in terms of numerical errors in the model or uncertainty in the measurements are attributed to the assumptions and simplifications of the physical model. Evaluation is critical to establishing both the acceptable uses and limitations of a model. Throughout its development, FDS has undergone various forms of evaluation, both at NIST and beyond. This guide provides a survey of work conducted to date to evaluate FDS. Roughly half of the referenced studies were aimed primarily at model evaluation, the other half describe limited work to validate FDS for a specific use. The latter group were performed mostly by practicing engineers who did not have the time or resources to comprehensively evaluate the model. Collectively, the body …
618 citations
TL;DR: In this article, a symmetry-preserving discretization of the Navier-Stokes equations is shown to be stable on any grid, and conserves the total mass, momentum and kinetic energy.
582 citations
Cites background or result from "Fully Conservative Higher Order Fin..."
...(101) in [4]) is identical to our fourth-order discretization....
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...[4] we take a 1⁄4 9=8 because all interpolations are fourth-order accurate then (on a uniform grid)....
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...[4] have considered a family of higher-order discretization schemes for incompressible flow that almost/fully conserve mass, momentum and kinetic energy....
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TL;DR: The overall numerical scheme obtained is highly suitable for the simulation of reactive turbulent flows in realistic geometries, for it combines arbitrarily high order of accuracy, discrete conservation of mass, momentum, and energy with consistent boundary conditions.
573 citations
Cites background from "Fully Conservative Higher Order Fin..."
...Keywords: High order scheme; Finite difference scheme; Low Mach number; Variable density; Energy conservation; Conservative scheme; Cylindrical coordinates; Boundary conditions; DNS; LES...
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...9....
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...As a result, quantities such as mass, momentum, or fuel mass fraction solved using a scalar transport equation are conserved discretely....
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TL;DR: In this paper, an eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor.
Abstract: An eddy-viscosity based, subgrid-scale model for large eddy simulations is derived from the analysis of the singular values of the resolved velocity gradient tensor. The proposed σ-model has, by construction, the property to automatically vanish as soon as the resolved field is either two-dimensional or two-component, including the pure shear and solid rotation cases. In addition, the model generates no subgrid-scale viscosity when the resolved scales are in pure axisymmetric or isotropic contraction/expansion. At last, it is shown analytically that it has the appropriate cubic behavior in the vicinity of solid boundaries without requiring any ad-hoc treatment. Results for two classical test cases (decaying isotropic turbulence and periodic channel flow) obtained from three different solvers with a variety of numerics (finite elements, finite differences, or spectral methods) are presented to illustrate the potential of this model. The results obtained with the proposed model are systematically equivalent or slightly better than the results from the Dynamic Smagorinsky model. Still, the σ-model has a low computational cost, is easy to implement, and does not require any homogeneous direction in space or time. It is thus anticipated that it has a high potential for the computation of non-homogeneous, wall-bounded flows.
502 citations
References
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TL;DR: In this article, a new eddy viscosity model is presented which alleviates many of the drawbacks of the existing subgrid-scale stress models, such as the inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes.
Abstract: One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.
6,747 citations
TL;DR: In this paper, a new technique is described for the numerical investigation of the time-dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier-Stokes equations are written in finite-difference form, and the solution is accomplished by finite-time step advancement.
Abstract: A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier‐Stokes equations are written in finite‐difference form, and the solution is accomplished by finite‐time‐step advancement The primary dependent variables are the pressure and the velocity components Also used is a set of marker particles which move with the fluid The technique is called the marker and cell method Some examples of the application of this method are presented All non‐linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired
5,841 citations
"Fully Conservative Higher Order Fin..." refers background or methods in this paper
...The standard second order accurate finite difference scheme [2] in a staggered grid system conserves kinetic energy and this scheme has proven useful for LES and DNS....
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...− S2)i is the standard divergence form in a staggered grid system [2]....
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TL;DR: In this article, a direct numerical simulation of a turbulent channel flow is performed, where the unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points.
Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.
4,788 citations
"Fully Conservative Higher Order Fin..." refers methods in this paper
...Filtered DNS data [22] at the same Reynolds number are plotted as a reference in the figures....
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Book•
01 Jan 1987TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Abstract: Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.
4,632 citations
TL;DR: In this paper, a methode numerique par volume fini pour the resolution des equations de Navier-Stokes bidimensionnelles, incompressible, and stationnaires, en coordonnees generales curvilignes, is presented.
Abstract: Presentation d'une methode numerique par volume fini pour la resolution des equations de Navier-Stokes bidimensionnelles, incompressibles, et stationnaires, en coordonnees generales curvilignes Application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur Comparaison des calculs avec des donnees experimentales
4,356 citations