A family of second order time stepping methods for the Darcy-Brinkman equations

Date

2019-04-01

Author

Cibik, Aytekin
Demir, Medine
Kaya Merdan, Songül

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

63
views

0
downloads

This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the idea of stabilizing the curvature for velocity, temperature and concentration equations. Accuracy in time is proven and the convergence results for the fully discrete solutions of problem variables are given. Several numerical examples including a convergence study are provided that support the derived theoretical results and demonstrate the efficiency and the accuracy of the method.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/34905

Journal

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

DOI

https://doi.org/10.1016/j.jmaa.2018.11.015

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

An analysis of a linearly extrapolated BDF2 subgrid artificial viscosity method for incompressible flows Demir, Medine (Elsevier BV, 2020-10-01) This report extends the mathematical support of a subgrid artificial viscosity (SAV) method to simulate the incompressible Navier-Stokes equations to better performing a linearly extrapolated BDF2 (BDF2LE) time discretization. The method considers the viscous term as a combination of the vorticity and the grad-div stabilization term. SAV method introduces global stabilization by adding a term, then anti-diffuses through the extra mixed variables. We present a detailed analysis of conservation laws, includin...
A DRBEM approximation of the Steklov eigenvalue problem Türk, Önder (Elsevier BV, 2021-01-01) In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all...
On the reduction principle for differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-12-01) In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297...
AN OPTIMAL-CONTROL PROBLEM WITH NONLINEAR ELLIPTIC STATE-EQUATIONS Leblebicioğlu, Mehmet Kemal (Elsevier BV, 1992-02-01) In this article some of the results for optimal control of linear systems have been generalized to a nonlinear case. This is achieved by employing standard techniques of the nonlinear theory. After demonstrating the existence of optimal controls, finite element method is used to discretize the problem. The resulting finite dimensional problem is solved by a special algorithm. The theoretical discussions are completed by proving that approximate solutions are reduced to exact solutions as the element size te...
Fundamental solution for coupled magnetohydrodynamic flow equations Bozkaya, Canan; Tezer, Münevver (Elsevier BV, 2007-06-01) In this paper, a fundamental solution for the coupled convection-diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and ind...

Citation Formats

A. Cibik, M. Demir, and S. Kaya Merdan, “A family of second order time stepping methods for the Darcy-Brinkman equations,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 148–175, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34905.