scholarly journals A framework to evaluate IMEX schemes for atmospheric models

2020 ◽  
Vol 13 (12) ◽  
pp. 6467-6480
Author(s):  
Oksana Guba ◽  
Mark A. Taylor ◽  
Andrew M. Bradley ◽  
Peter A. Bosler ◽  
Andrew Steyer
Keyword(s):  
Acoustic Waves ◽  
Normal Modes ◽  
Evaluation Framework ◽  
Acoustic System ◽  
Time Stepping ◽  
Imex Schemes ◽  
Runge Kutta ◽  
The Stability ◽  
Implicit And Explicit ◽  
New Framework

Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

scholarly journals A framework to evaluate IMEX schemes for atmospheric models

2020 ◽  
Author(s):  
Oksana Guba ◽  
Mark A. Taylor ◽  
Andrew M. Bradley ◽  
Peter A. Bosler ◽  
Andrew Steyer
Keyword(s):  
Acoustic Waves ◽  
Normal Modes ◽  
Evaluation Framework ◽  
Acoustic System ◽  
Atmospheric Models ◽  
Imex Methods ◽  
Imex Schemes ◽  
Runge Kutta ◽  
Implicit And Explicit ◽  
New Framework

Abstract. We present a new evaluation framework for implicit and explicit (IMEX) Runge-Kutta timestepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate stability of IMEX methods and their dispersion and dissipation for gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of 2nd order low-storage IMEX Runge-Kutta methods with high CFL. We show that the new framework is more selective than the 2D acoustic system previously used in literature. Schemes that are stable for the 2D acoustic system are not stable for the system of normal modes.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part I: Implicit Runge–Kutta Schemes

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Graham Ashcroft ◽  
Christian Frey ◽  
Kathrin Heitkamp ◽  
Christian Weckmüller
Keyword(s):  
Stokes Equations ◽  
Temporal Integration ◽  
Aerodynamic Noise ◽  
Navier Stokes ◽  
Noise Generation ◽  
Academic Problems ◽  
Tonal Noise ◽  
Navier Stokes Equations ◽  
Runge Kutta ◽  
The Stability

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Real-time completion monitoring with acoustic waves

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. E15-E33 ◽  
Author(s):  
Andrey Bakulin ◽  
Alexander Sidorov ◽  
Boris Kashtan ◽  
Mikko Jaaskelainen
Keyword(s):  
Real Time ◽  
Acoustic Waves ◽  
Acoustic System ◽  
Acoustic Signatures ◽  
New Findings ◽  
Sand Control ◽  
Surveillance Method ◽  
4D Seismic ◽  
Permeability Impairment ◽  
Downhole Sensors

Deepwater production is challenged by well underperformance issues that are hard to diagnose early on and expensive to deal with later. Problems are amplified by reliance on a few complex wells with sophisticated sand-control media. New downhole data are required for better understanding and prevention of production impairment. We introduce real-time completion monitoring (RTCM), a new nonintrusive surveillance method that uses acoustic signals sent via the fluid column to identify permeability impairment in sand-screened completions. The signals are carried by tube waves that move borehole fluid back and forth radially across the completion layers. Such tube waves are capable of instant testing of the presence or absence of fluid communication across the completion and are sensitive to changes occurring in sand screens, gravel sand, perforations, and possibly in the reservoir. The part of the completion that has different impairment from its neighbors will carry tube waves with modified signatures (velocity, attenuation) and will produce a reflection from the boundary where impairment changes. We conduct a laboratory experiment with a model of a completed horizontal borehole and focus on effects of sand-screen permeability on transmitted and reflected acoustic signatures. These new findings form the basis of an RTCM method that can be thought of as “miniaturized” 4D seismic and as a “permanent log” in an individual wellbore. We present experiments with a fiber-optic acoustic system that suggest a nonintrusive way to install downhole sensors on the pipe in realistic completions and thus implement real-time surveillance with RTCM.

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

scholarly journals Multigrid and Runge-Kutta time stepping applied to the uniformly non-oscillatory scheme for conservation laws

1991 ◽  
Vol 25 (3) ◽  
pp. 243-263 ◽  
Author(s):  
J. W. van der Burg ◽  
J. G. M. Kuerten ◽  
P. J. Zandbergen
Keyword(s):  
Conservation Laws ◽  
Time Stepping ◽  
Runge Kutta

scholarly journals Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

scholarly journals A General Framework for Implicit and Explicit Debiasing of Distributional Word Vector Spaces

2020 ◽  
Vol 34 (05) ◽  
pp. 8131-8138
Author(s):  
Anne Lauscher ◽  
Goran Glavaš ◽  
Simone Paolo Ponzetto ◽  
Ivan Vulić
Keyword(s):  
General Framework ◽  
Semantic Information ◽  
Evaluation Framework ◽  
Vector Spaces ◽  
Racial Biases ◽  
Definition Of ◽  
Cross Lingual ◽  
Experimental Findings ◽  
Implicit And Explicit ◽  
Embedding Methods

Distributional word vectors have recently been shown to encode many of the human biases, most notably gender and racial biases, and models for attenuating such biases have consequently been proposed. However, existing models and studies (1) operate on under-specified and mutually differing bias definitions, (2) are tailored for a particular bias (e.g., gender bias) and (3) have been evaluated inconsistently and non-rigorously. In this work, we introduce a general framework for debiasing word embeddings. We operationalize the definition of a bias by discerning two types of bias specification: explicit and implicit. We then propose three debiasing models that operate on explicit or implicit bias specifications and that can be composed towards more robust debiasing. Finally, we devise a full-fledged evaluation framework in which we couple existing bias metrics with newly proposed ones. Experimental findings across three embedding methods suggest that the proposed debiasing models are robust and widely applicable: they often completely remove the bias both implicitly and explicitly without degradation of semantic information encoded in any of the input distributional spaces. Moreover, we successfully transfer debiasing models, by means of cross-lingual embedding spaces, and remove or attenuate biases in distributional word vector spaces of languages that lack readily available bias specifications.

Sign in / Sign up

Export Citation Format

Share Document