Sensitivity of a marine coupled physical biogeochemical model to time resolution, integration scheme and time splitting method

2012 ◽  
Vol 52-53 ◽  
pp. 36-53 ◽  
Author(s):  
Momme Butenschön ◽  
Marco Zavatarelli ◽  
Marcello Vichi
Keyword(s):  
Time Resolution ◽  
Splitting Method ◽  
Integration Scheme ◽  
Biogeochemical Model ◽  
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.

scholarly journals Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

2018 ◽  
Author(s):  
Tuomas Kärnä ◽  
Stephan C. Kramer ◽  
Lawrence Mitchell ◽  
David A. Ham ◽  
Matthew D. Piggott ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Unstructured Grid ◽  
Splitting Method ◽  
Time Integration ◽  
River Estuary ◽  
Coastal Ocean ◽  
Second Order ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Element Discretization

Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

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.

scholarly journals Efficient time-splitting Hermite-Galerkin spectral method for the coupled nonlinear Schrödinger equations

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Qingqu Zhuang ◽  
Yi Yang
Keyword(s):  
Splitting Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Time Step ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Time Splitting ◽  
Coupled Nonlinear Schrodinger Equations

The paper focuses on efficient time-splitting Hermite-Galerkin spectral approximation of the coupled nonlinear Schrödinger equations on the whole line. The original problem is decomposed into one nonlinear subproblem and one linear subproblem by time-splitting method. At each time step, the nonlinear subproblem is solved exactly. While the linear subproblem is efficiently solved by choosing suitable Hermite basis functions with matrix decomposition technique. Numerical experiments are carried out to demonstrate the effectiveness and efficiency of the proposed method.

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