arXiv subjects

Songul Kaya

Publications and source records attributed to Songul Kaya.

5 recordsLinked to original sources

arXiv2026

Improved Arrow-Hurwicz method for Stationary Inductionless Magnetohydrodynamics System

In this work, we propose a new Arrow-Hurwicz iterative scheme designed to solve the steady inductionless magnetohydrodynamics system. The main feature of the proposed scheme is the introduction of new penalty terms in the current density equation. These terms play a central role in effectively controlling the unfavorable mixed terms that commonly arise in such formulations. The proposed method is shown to achieve geometric convergence. Numerical tests affirm the efficiency of the new scheme without compromising accuracy.

math.NA↗

arXiv2019

Numerical analysis of an efficient second order time filtered backward Euler method for MHD equations

The present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the system. Since time filters for fluid variables are added as separate post processing steps, the method can be easily incorporated into an existing backward Euler code. We investigate the conservation and long time stability properties of the improved scheme. Stability and second order convergence of the method are also proven. The influences of introduced time filter method on several numerical experiments are given, which both verify the theoretical findings and illustrate its usefulness on practical problems.

math.NA↗

arXiv2018

Long time stability of a linearly extrapolated blended BDF scheme for multiphysics flows

This paper investigates the long time stability behavior of multiphysics flow problems, namely the Navier-Stokes equations, natural convection and double-diffusive convection equations with an extrapolated blended BDF time-stepping scheme. This scheme combines the two-step BDF and three-step BDF time stepping schemes. We prove unconditional long time stability theorems for each of flow systems. Various numerical tests are given for large time step sizes in long time intervals in order to support theoretical results.

math.NA↗

arXiv2018

A Family of Second Order Time Stepping Methods for the Darcy-Brinkman Equations

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.

math.NA↗

arXiv2017

A Modular Regularized Variational Multiscale Proper Orthogonal Decomposition for Incompressible Flows

In this paper, we propose, analyze and test a post-processing implementation of a projection-based variational multiscale (VMS) method with proper orthogonal decomposition (POD) for the incompressible Navier-Stokes equations. The projection-based VMS stabilization is added as a separate post-processing step to the standard POD approximation, and since the stabilization step is completely decoupled, the method can easily be incorporated into existing codes, and stabilization parameters can be tuned independent from the time evolution step. We present a theoretical analysis of the method, and give results for several numerical tests on benchmark problems which both illustrate the theory and show the proposed method's effectiveness.

math.NA↗