Numerical analysis of a Family of Second Order Time Stepping Methods for Boussinesq Equations

Date

2018-07-06

Author

Çıbık, Aytekin Bayram
Demir, Medine
Kaya Merdan, Songül

Metadata

Show full item record

Item Usage Stats

178
views

0
downloads

—This report considers a family of second order time stepping schemes for Boussinesq system. The scheme uses the idea of curvature stabilization in which the discrete curvature of the solutions is added together with the linearized advective term at each time step. Unconditional stability and convergence of the method are established. Several numerical experiments are provided to demonstrate the accuracy and the efficiency of the method.

Subject Keywords

Boussinesq equations, Curvature stabilization, Linear extrapolation, Error analysis

URI

http://www.iaeng.org/publication/WCE2018/WCE2018_pp56-59.pdf
https://hdl.handle.net/11511/78323

Conference Name

Proceedings of the World Congress on Engineering 2018 Vol I WCE 2018, (July 4-6, 2018)

Collections

Department of Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization Hacat, Gülnur; Yılmaz, Fikriye Nuray; Çıbık, Aytekin Bayram; Kaya Merdan, Songül (2022-10-01) © 2022 Elsevier Inc.This paper presents a family of implicit-explicit (IMEX) time stepping scheme for the optimal control problem of the unsteady Navier-Stokes equations (NSE). The main feature of this kind of optimal control problem is that stabilization terms are proportional to discrete curvature of the solutions. First and second order optimality conditions are used for optimality of the curvature based stabilized Navier-Stokes equations. Complete stability and error analyses of state, adjoint and contr...
Greedy Reduction Algorithms for Mixtures of Exponential Family Ardeshiri, Tohid; Granstrom, Karl; Özkan, Emre; Orguner, Umut (2015-06-01) In this letter, we propose a general framework for greedy reduction of mixture densities of exponential family. The performances of the generalized algorithms are illustrated both on an artificial example where randomly generated mixture densities are reduced and on a target tracking scenario where the reduction is carried out in the recursion of a Gaussian inverse Wishart probability hypothesis density (PHD) filter.
Effective preconditioners for large integral-equation problems Malas, T.; Ergül, Özgür Salih; Gürel, L. (2007-11-16) We consider effective preconditioning schemes for the iterative solution of integral-equation methods. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximatio...
Development of dispute prediction and resolution method selection models for construction disputes Ayhan, Mura; Birgönül, Mustafa Talat; Department of Civil Engineering (2019) Construction industry is overwhelmed by increasing number and severity of disputes proving that current practices are insufficient in avoidance. This research argues that in order to forestall and mitigate construction disputes, prediction models should be developed by utilizing machine learning algorithms. The research suggests developing three distinct models; (1) dispute occurrence prediction model, (2) potential compensation prediction model, and (3) resolution method selection model. For this reason, a...
Error exponents for variable-length block codes with feedback and cost constraints Nakiboğlu, Barış (Institute of Electrical and Electronics Engineers (IEEE), 2008-03-01) Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error P-e,P-min as a function of constraints R, P, and T on the transmission rate, average cost, and average block length, respectively. For given R and P, the lower and upper bounds to the exponent -(In P-e,P-min)/(T) over bar are asymptotically equal as (T) over bar -> infinity. The resulting r...

Citation Formats

A. B. Çıbık, M. Demir, and S. Kaya Merdan, “Numerical analysis of a Family of Second Order Time Stepping Methods for Boussinesq Equations,” London, U.K., 2018, vol. 1, Accessed: 00, 2021. [Online]. Available: http://www.iaeng.org/publication/WCE2018/WCE2018_pp56-59.pdf.