A compressible Navier-Stokes code for turbulent flow modeling

An implicit, finite volume code for solving two dimensional, compressible turbulent flows is described. Second order upwind differencing of the inviscid terms of the equations is used to enhance stability and accuracy. A diagonal form of the implicit algorithm is used to improve efficiency. Several zero and two equation turbulence models are incorporated to study their impact on overall flow modeling accuracy. Applications to external and internal flows are discussed

Impact of turbulence modeling on numerical accuracy and efficiency of compressible flow simulations

Discussed is the numerical implementation of turbulence models used in viscous compressible flow simulations and their performance described with respect to numerical accuracy, efficiency and stability. The basic approach utilizes the Reynolds-averaged compressible Navier-Stokes equations in which the Reynolds stresses and heat fluxes are mathematically modeled by suitable turbulence models. The turbulence models investigated include zero-, one-, and two-equation eddy viscosity models. The flow fields investigated include theoretical and supersonic flows about two-dimensional and axisymmetric bodies. Discussions concerning the numerical implementation of models include differencing procedures and boundary conditions used to assume numerical stability and accuracy. Numerical performance is also evaluated by comparing computations with experimental results

A generalized averaging method for linear differential equations with almost periodic coefficients

Generalized averaging method for linear differential equations with almost periodic coefficient

Markov-Switching GARCH Modelling of Value-at-RisK

This paper proposes an asymmetric Markov regime-switching (MS) GARCH model to estimate value-at-risk (VaR) for both long and short positions. This model improves on existing VaR methods by taking into account both regime change and skewness or leverage effects. The performance of our MS model and single-regime models is compared through an innovative backtesting procedure using daily data for UK and US market stock indices. The findings from exceptions and regulatory-based tests indicate the MS-GARCH specifications clearly outperform other models in estimating the VaR for both long and short FTSE positions and also do quite well for S&P positions. We conclude that ignoring skewness and regime changes has the effect of imposing larger than necessary conservative capital requirements

Turbulence modeling for hypersonic flows

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed

The Origin and Evolution of a Complex Cuspate Foreland: Pointe-aux-Pins, Lake Erie, Ontario

The origin of Pointe-aux-Pins, a large, rounded, cuspate foreland protruding from the north shore of Lake Erie, is difficult to explain by conventional spit formation processes. Stratigraphic evidence from boreholes, the distribution of nearshore sediments, surface geomorphology, and previously published interpretations of Lake Erie water levels were combined to produce an hypothetical model of the development of the foreland from approximately 12,000 years BP to now. According to the model, the ancestral Pointe-aux-Pins began as a promontory caused by the intersection of the cross-lake Erieau moraine with the original lake shoreline, then located tens of kilometres lakeward of its present position. Lake levels at the time were about 30 m below present datum (173.3 m a.s.l.). Modern Pointe-aux-Pins dates from after the Nipissing "flood", at about 3500 BP, when the thereto-submerged sandy spit platform was again subjected to wave action, leading to beach ridge and dune formation. The age of the foreland of 3500 to 4000 years compares well with estimates based on the annual sand supply rate and the present sand volume in Pointe-aux-Pins.L'origine de la pointe aux Pins, vaste avancée triangulaire arquée sur la rive septentrionale du lac Érié, est difficile à expliquer par les processus courants de formation des flèches littorales. Les éléments de preuves d'ordre stratigraphique trouvés dans les trous de forage, la répartition des sédiments sur le littoral, la géomorphologie des formations superficielles et les interprétations déjà publiées sur les niveaux du lac Érié ont été combinés afin de créer un modèle hypothétique de l'évolution de cette pointe de terre, depuis environ 12 000 ans BP. Selon le modèle, l'ancienne pointe aux Pins a d'abord été un promontoire qui s'est formé à l'intersection de la moraine d'Erieau et du rivage originel du lac, alors situé à des dizaines de kilomètres au large. Le niveau du lac était alors à 30 m au-dessous de la surface actuelle (173,3 m a.n.m.). L'actuelle pointe aux Pins est postérieure à « l'inondation » de Nipissing, survenue il y a environ 3500 ans BP, lorsque la plate-forme constituée par la flèche de sable a de nouveau été soumise à l'action des vagues, ce qui a entraîné la formation de crêtes de plage et de dunes. L'âge de 3500-4000 ans attribué à la pointe de terre correspond bien aux estimations fondées sur le taux annuel d'apport en sable et le volume actuel de sable à la pointe aux Pins.Der Ursprung von Pointe-aux-Pins, einem breiten, geschweiften dreieckigen Strandvorsprung, der aus dem Nordufer des Erie-Sees herausragt, ist nicht einfach aus den ùblichen Prozessen der Landspitzenbildung zu erklâren. Stratigraphische Nachweise aus Bohrlôchern, die Verteilung von kùstennahen Sedimenten, die Oberflàchengeomorphologie und frûher verôffentlichte Interpretationen der Wasserspiegel des Erie-Sees wurden kombiniert, um ein hypothetisches Modell der Entwicklung des Strandvorsprungs von etwa 12 000 v.u.Z. bis heute zu entwickeln. Aus dem Modell geht hervor, dass die Ur-Pointe-aux-Pins-Landzunge als ein Vorgebirge begann, das sich am Schnittpunkt der quer durch den See verlaufenden Erieau-Moràne mit der ursprùnglichen Seekùste bildete, die sich damais 10 km seeeinwàrts von ihrer heutigen Position befand. Der Seewasserspiegel war damais etwa 30 m unter dem gegenwàrtigen (173.3 m ù.M.). Die heutige Pointe-aux-Pins-Landzunge stammt aus derZeit nach der "Ùberflutung" von Nipissing um ungefahr 3500 v.u.Z., als die hoch dazu untergetauchte Sandlandspitze wieder dem Einfluss der Wellen ausgesetzt war, was zur Bildung von Strandkâmmen und Dùnen fùhrte. Das Alter des Strandvorsprungs von 3550 bis 4000 Jahren stimmt gut ùberein mit den auf die jahrliche Sandzufuhrrate und das gegenwârtige Sandvolumen gestùtzten Schatzungen in Pointe-aux-Pins

Assessment of closure coefficients for compressible-flow turbulence models

A critical assessment is made of the closure coefficients used for turbulence length scale in existing models of the transport equation, with reference to the extension of these models to compressible flow. It is shown that to satisfy the compressible 'law of the wall', the model coefficients must actually be functions of density gradients. The magnitude of the errors that result from neglecting this dependence on density varies with the variable used to specify the length scale. Among the models investigated, the k-omega model yields the best performance, although it is not completely free from errors associated with density terms. Models designed to reduce the density-gradient effect to an insignificant level are proposed

An assessment and application of turbulence models for hypersonic flows

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models