scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

Integration of CFD to Design Experiments for Enhanced Spatial and Temporal Discretization

2017 ◽  
Author(s):  
C. De Maesschalck ◽  
S. Lavagnoli ◽  
G. Paniagua
Keyword(s):  
Measurement Errors ◽  
A Priori ◽  
A Priori Estimate ◽  
Spatial Sampling ◽  
Navier Stokes ◽  
Implicit Time ◽  
Time Averaging ◽  
Time Resolved ◽  
Downstream Flow ◽  
The Individual

The availability of high fidelity Computational Fluid Dynamics (CFD) suitable for turbomachinery design offers a powerful tool to define an effective experimental measurement campaign. This paper describes approaches to integrate Reynolds-Averaged Navier-Stokes simulations into experiment design. CFD simulations are used to a priori estimate the measurement errors induced by the finite spatial sampling and inherent limited sensor bandwidth for space-resolved and time-resolved turbine aerothermal measurements. The CFD predictions are employed to optimize the probe placement and traversing while minimizing the measurement errors associated with the finite spatial sampling. Additionally, time-resolved CFD traces serve to quantify the measurement errors as a function of the measurement chain bandwidth. This approach was applied to a recent turbine test program, focused on the aerothermal characterization of the turbine over-tip casing endwall and downstream flow field. Based on the 3D simulations of the different rotor geometries, the discrete radial positions of the aerothermal probes located downstream of the stage were optimized to minimize the uncertainty on the individual aerodynamic quantities, as well as to mitigate the propagated uncertainty on the turbine loss coefficient. Furthermore, the effect of the implicit time-averaging of all sensors, due to the limited frequency response, was quantified. This manuscript illustrates the benefits of CFD in the design and planning of a turbine experimental campaign. Based on the proposed procedure, the experimentalist can find the best compromise between measurement precision and instrumentation costs by establishing the minimum sensor performance requirements to obtain the target accuracies.

scholarly journals Fast-Projection Methods for the Incompressible Navier–Stokes Equations

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 222
Author(s):  
Carlo De Michele ◽  
Francesco Capuano ◽  
Gennaro Coppola
Keyword(s):  
Stokes Equations ◽  
Time Integration ◽  
Turbulent Channel Flow ◽  
Projection Methods ◽  
Navier Stokes ◽  
Time Step ◽  
Order Accuracy ◽  
Navier Stokes Equations ◽  
Pressure Poisson Equation ◽  
Special Cases

An analysis of existing and newly derived fast-projection methods for the numerical integration of incompressible Navier–Stokes equations is proposed. Fast-projection methods are based on the explicit time integration of the semi-discretized Navier–Stokes equations with a Runge–Kutta (RK) method, in which only one Pressure Poisson Equation is solved at each time step. The methods are based on a class of interpolation formulas for the pseudo-pressure computed inside the stages of the RK procedure to enforce the divergence-free constraint on the velocity field. The procedure is independent of the particular multi-stage method, and numerical tests are performed on some of the most commonly employed RK schemes. The proposed methodology includes, as special cases, some fast-projection schemes already presented in the literature. An order-of-accuracy analysis of the family of interpolations here presented reveals that the method generally has second-order accuracy, though it is able to attain third-order accuracy only for specific interpolation schemes. Applications to wall-bounded 2D (driven cavity) and 3D (turbulent channel flow) cases are presented to assess the performances of the schemes in more realistic configurations.

Research and analysis of business management processes implemented under conditions of incomplete certainty

2020 ◽  
Author(s):  
Igor Klimenko ◽  
A. Ivlev
Keyword(s):  
Decision Making ◽  
A Priori ◽  
Business Management ◽  
Statistical Uncertainty ◽  
Management Processes ◽  
Classical Decision ◽  
Decision Making Criteria

The study carried out in this work made it possible to expand the rank scale for a priori assessment of the chosen strategy in terms of increasing the sensitivity of assessing the caution / negligence ratio using risky, as well as classical decision-making criteria under conditions of statistical uncertainty.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

scholarly journals Communities and the individual: Beyond the liberal–communitarian divide

2021 ◽  
Vol 47 (4) ◽  
pp. 392-401
Author(s):  
Volker Kaul
Keyword(s):  
Personal Autonomy ◽  
A Priori ◽  
Significant Others ◽  
The Self ◽  
Global Perspective ◽  
Self And Identity ◽  
Default Position ◽  
The Individual

Liberalism believes that individuals are endowed a priori with reason or at least agency and it is up to that reason and agency to make choices, commitments and so on. Communitarianism criticizes liberalism’s explicit and deliberate neglect of the self and insists that we attain a self and identity only through the effective recognition of significant others. However, personal autonomy does not seem to be a default position, neither reason nor community is going to provide it inevitably. Therefore, it is so important to go beyond the liberal–communitarian divide. This article is analysing various proposals in this direction, asks about the place of communities and the individual in times of populism and the pandemic and provides a global perspective on the liberal–communitarian debate.

scholarly journals Detailed Modeling of Cork-Phenolic Ablators in Preparation for the Post-flight Analysis of the QARMAN Re-entry CubeSat

2021 ◽  
Author(s):  
Claudio Miccoli ◽  
Alessandro Turchi ◽  
Pierre Schrooyen ◽  
Domenic D’Ambrosio ◽  
Thierry Magin
Keyword(s):  
Fluid Dynamics ◽  
Thermal Protection ◽  
A Priori ◽  
European Space Agency ◽  
Thermal Response ◽  
Accurate Method ◽  
Navier Stokes ◽  
Advection Equation ◽  
High Enthalpy ◽  
Space Agency

AbstractThis work deals with the analysis of the cork P50, an ablative thermal protection material (TPM) used for the heat shield of the qarman Re-entry CubeSat. Developed for the European Space Agency (ESA) at the von Karman Institute (VKI) for Fluid Dynamics, qarman is a scientific demonstrator for Aerothermodynamic Research. The ability to model and predict the atypical behavior of the new cork-based materials is considered a critical research topic. Therefore, this work is motivated by the need to develop a numerical model able to respond to this demand, in preparation to the post-flight analysis of qarman. This study is focused on the main thermal response phenomena of the cork P50: pyrolysis and swelling. Pyrolysis was analyzed by means of the multi-physics Computational Fluid Dynamics (CFD) code argo, developed at Cenaero. Based on a unified flow-material solver, the Volume Averaged Navier–Stokes (VANS) equations were numerically solved to describe the interaction between a multi-species high enthalpy flow and a reactive porous medium, by means of a high-order Discontinuous Galerkin Method (DGM). Specifically, an accurate method to compute the pyrolysis production rate was implemented. The modeling of swelling was the most ambitious task, requiring the development of a physical model accounting for this phenomenon, for the purpose of a future implementation within argo. A 1D model was proposed, mainly based on an a priori assumption on the swelling velocity and the resolution of a nonlinear advection equation, by means of a Finite Difference Method (FDM). Once developed, the model was successfully tested through a matlab code, showing that the approach is promising and thus opening the way to further developments.

scholarly journals Sartres Lösung zur Antinomie der sozialen Realität in der Kritik der dialektischen Vernunft

2020 ◽  
Vol 68 (6) ◽  
pp. 817-847
Author(s):  
Sebastian Gardner
Keyword(s):  
Ethical Theory ◽  
A Priori ◽  
Social Ontology ◽  
Human Freedom ◽  
Philosophical Foundation ◽  
A Posteriori ◽  
Political Reality ◽  
Dialectical Reason ◽  
The Individual

AbstractCritics have standardly regarded Sartre’s Critique of Dialectical Reason as an abortive attempt to overcome the subjectivist individualism of his early philosophy, motivated by a recognition that Being and Nothingness lacks ethical and political significance, but derailed by Sartre’s Marxism. In this paper I offer an interpretation of the Critique which, if correct, shows it to offer a coherent and highly original account of social and political reality, which merits attention both in its own right and as a reconstruction of the philosophical foundation of Marxism. The key to Sartre’s theory of collective and historical existence in the Critique is a thesis carried over from Being and Nothingness: intersubjectivity on Sartre’s account is inherently aporetic, and social ontology reproduces in magnified form its limited intelligibility, lack of transparency, and necessary frustration of the demands of freedom. Sartre’s further conjecture – which can be formulated a priori but requires a posteriori verification – is that man’s collective historical existence may be understood as the means by which the antinomy within human freedom, insoluble at the level of the individual, is finally overcome. The Critique provides therefore the ethical theory promised in Being and Nothingness.

scholarly journals A two-dimensional glacier–fjord coupled model applied to estimate submarine melt rates and front position changes of Hansbreen, Svalbard

2018 ◽  
Vol 64 (247) ◽  
pp. 745-758 ◽  
Author(s):  
E. DE ANDRÉS ◽  
J. OTERO ◽  
F. NAVARRO ◽  
A. PROMIŃSKA ◽  
J. LAPAZARAN ◽  
...  
Keyword(s):  
Coupled Model ◽  
Small Scale ◽  
Two Dimensional ◽  
Time Step ◽  
Software Packages ◽  
Front Position ◽  
Circulation Patterns ◽  
Glacier Front ◽  
Order Of Magnitude ◽  
Frontal Ablation

ABSTRACTWe have developed a two-dimensional coupled glacier–fjord model, which runs automatically using Elmer/Ice and MITgcm software packages, to investigate the magnitude of submarine melting along a vertical glacier front and its potential influence on glacier calving and front position changes. We apply this model to simulate the Hansbreen glacier–Hansbukta proglacial–fjord system, Southwestern Svalbard, during the summer of 2010. The limited size of this system allows us to resolve some of the small-scale processes occurring at the ice–ocean interface in the fjord model, using a 0.5 s time step and a 1 m grid resolution near the glacier front. We use a rich set of field data spanning the period April–August 2010 to constrain, calibrate and validate the model. We adjust circulation patterns in the fjord by tuning subglacial discharge inputs that best match observed temperature while maintaining a compromise with observed salinity, suggesting a convectively driven circulation in Hansbukta. The results of our model simulations suggest that both submarine melting and crevasse hydrofracturing exert important controls on seasonal frontal ablation, with submarine melting alone not being sufficient for reproducing the observed patterns of seasonal retreat. Both submarine melt and calving rates accumulated along the entire simulation period are of the same order of magnitude, ~100 m. The model results also indicate that changes in submarine melting lag meltwater production by 4–5 weeks, which suggests that it may take up to a month for meltwater to traverse the englacial and subglacial drainage network.

A finite element method for the Navier-Stokes equations in moving domain with application to hemodynamics of the left ventricle

2017 ◽  
Vol 32 (4) ◽  
Author(s):  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Yuri Vassilevski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Left Ventricle ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Computed Tomography Images ◽  
Time Dependent Domain ◽  
Element Method

AbstractThe paper introduces a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method is based on a quasi-Lagrangian formulation of the problem and handling the geometry in a time-explicit way. We prove that numerical solution satisfies a discrete analogue of the fundamental energy estimate. This stability estimate does not require a CFL time-step restriction. The method is further applied to simulation of a flow in a model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.

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