Numerical Analysis of Second Order Time Stepping Methods for the Natural Convection Problems

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2018-06-27

Author

Demir, Medine
Kaya Merdan, Songül

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https://hdl.handle.net/11511/76823

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Numerical analysis of a projection-based stabilization method for the natural convection problems Çıbık, Aytekin Bayram; Kaya Merdan, Songül; Department of Mathematics (2011) In this thesis, we consider a projection-based stabilization method for solving buoyancy driven flows (natural convection problems). The method consists of adding global stabilization for all scales and then anti-diffusing these effects on the large scales defined by projections into appropriate function spaces. In this way, stabilization acts only on the small scales. We consider two different variations of buoyancy driven flows based on the projection-based stabilization. First, we focus on the steady-sta...
Numerical analysis of a Family of Second Order Time Stepping Methods for Boussinesq Equations Çıbık, Aytekin Bayram; Demir, Medine; Kaya Merdan, Songül (null; 2018-07-06) —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.
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Numerical methods for the solution of the neoclassical growth model Dedeoğlu, Bülent; Ekinci, Nazım; Department of Economics (1999)
Numerical solution of semi-linear advection-diffusion-reaction equations by discontinuous galerkin methods Yıldız, Süleyman; Karasözen, Bülent; Department of Scientific Computing (2016) IIn this thesis, we study splitting methods for semi-linear advection-diffusion-reaction (ADR) equations which are discretized by the symmetric interior penalty Galerkin (SIPG) method in space. For the time integration Rosenbrock methods are used with Strang splitting. The linear system of equations are solved iteratively by preconditioned generalized minimum residual method (GMRES). Numerical experiments for ADR equations with different type nonlinearities demonstrate the effectiveness of the proposed appr...

Citation Formats

M. Demir and S. Kaya Merdan, “Numerical Analysis of Second Order Time Stepping Methods for the Natural Convection Problems,” 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/76823.