On steady state computation of turbulent flows usingk–ɛ models approximated by the time splitting method

2006 ◽  
Vol 51 (1) ◽  
pp. 77-115
Author(s):  
Tao Du ◽  
Zi-Niu Wu ◽  
Bing Wang
Keyword(s):  
Steady State ◽  
Turbulent Flows ◽  
Splitting Method ◽  
Time Splitting

Convergence of time-splitting approximations for degenerate convection-diffusion equations with a random source

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Roberto Díaz-Adame ◽  
Silvia Jerez
Keyword(s):  
Hyperbolic Conservation Laws ◽  
Splitting Method ◽  
Diffusion Equations ◽  
Hyperbolic Conservation ◽  
Convection Diffusion ◽  
Parabolic Case ◽  
Weak Entropy Solution ◽  
Degenerate Parabolic ◽  
Time Splitting ◽  
Operator Scheme

AbstractIn this paper we propose a time-splitting method for degenerate convection-diffusion equations perturbed stochastically by white noise. This work generalizes previous results on splitting operator techniques for stochastic hyperbolic conservation laws for the degenerate parabolic case. The convergence in $\begin{array}{} \displaystyle L^p_{loc} \end{array}$ of the time-splitting operator scheme to the unique weak entropy solution is proven. Moreover, we analyze the performance of the splitting approximation by computing its convergence rate and showing numerical simulations for some benchmark examples, including a fluid flow application in porous media.

A Numerical Study of Quantum Decoherence

2012 ◽  
Vol 12 (1) ◽  
pp. 85-108 ◽  
Author(s):  
Riccardo Adami ◽  
Claudia Negulescu
Keyword(s):  
Density Matrix ◽  
Particle Density ◽  
Numerical Study ◽  
Heavy Particle ◽  
Splitting Method ◽  
Time Dependent ◽  
Quantum Decoherence ◽  
Approximation Formula ◽  
Time Splitting ◽  
Decoherence Effect

AbstractThe present paper provides a numerical investigation of the decoherence effect induced on a quantum heavy particle by the scattering with a light one. The time dependent two-particle Schrödinger equation is solved by means of a time-splitting method. The damping undergone by the non-diagonal terms of the heavy particle density matrix is estimated numerically as well as the error in the Joos-Zeh approximation formula.

scholarly journals Alternating direction implicit type preconditioners for the steady state inhomogeneous Vlasov equation

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Markus Gasteiger ◽  
Lukas Einkemmer ◽  
Alexander Ostermann ◽  
David Tskhakaya
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Vlasov Equation ◽  
Numerical Solutions ◽  
Splitting Method ◽  
Time Integration ◽  
Computational Effort ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Wide Range

The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov-based methods such as the generalized minimal residual method (GMRES) or relaxation schemes) is computationally expensive. In the former case the slowest time scale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an alternating direction implicit type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speed-up of close to two orders of magnitude (even for intermediate grid sizes) with respect to the unpreconditioned case. In addition, we discuss the characteristics of these numerical methods and show the results for a number of numerical simulations.

scholarly journals Condensates in thin-layer turbulence

2019 ◽  
Vol 864 ◽  
pp. 490-518 ◽  
Author(s):  
Adrian van Kan ◽  
Alexandros Alexakis
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Turbulent Flows ◽  
Mean Field ◽  
Direct Numerical Simulations ◽  
Thin Layers ◽  
Scale Model ◽  
Two Dimensional ◽  
Critical Height ◽  
Basic Features

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.

scholarly journals Assessment of Hydrometeor Collection Rates from Exact and Approximate Equations. Part II: Numerical Bounding

2007 ◽  
Vol 46 (1) ◽  
pp. 82-96
Author(s):  
Brian J. Gaudet ◽  
Jerome M. Schmidt
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Splitting Method ◽  
Time Discretization ◽  
Large Mass ◽  
Time Step ◽  
Transfer Rates ◽  
Mass Moment ◽  
Time Splitting ◽  
Approximate Equations

Abstract Past microphysical investigations, including Part I of this study, have noted that the collection equation, when applied to the interaction between different hydrometeor species, can predict large mass transfer rates, even when an exact solution is used. The fractional depletion in a time step can even exceed unity for the collected species with plausible microphysical conditions and time steps, requiring “normalization” by a microphysical scheme. Although some of this problem can be alleviated through the use of more moment predictions and hydrometeor categories, the question as to why such “overdepletion” can be predicted in the first place remains insufficiently addressed. It is shown through both physical and conceptual arguments that the explicit time discretization of the bulk collection equation for any moment is not consistent with a quasi-stochastic view of collection. The result, under certain reasonable conditions, is a systematic overprediction of collection, which can become a serious error in the prediction of higher-order moments in a bulk scheme. The term numerical bounding is used to refer to the use of a quasi-stochastically consistent formula that prevents fractional collections exceeding unity for any moments. Through examples and analysis it is found that numerical bounding is typically important in mass moment prediction for time steps exceeding approximately 10 s. The Poisson-based numerical bounding scheme is shown to be simple in application and conceptualization; within a straightforward idealization it completely corrects overdepletion while even being immune to the rediagnosis error of the time-splitting method. The scheme’s range of applicability and utility are discussed.

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