Error analysis of a time-splitting method for incompressible flows with variable density

2020 ◽  
Vol 150 ◽  
pp. 384-395 ◽  
Author(s):  
Rong An
Keyword(s):  
Error Analysis ◽  
Incompressible Flows ◽  
Splitting Method ◽  
Variable Density ◽  
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 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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