A Projection-Based VMS Method on Linearly Extrapolated BDF2Time-stepping Scheme for Navier-Stokes Equations



A spectral collocation algorithm for two-point boundary value problem in fiber Raman amplifier equations
Tarman, Işık Hakan (Elsevier BV, 2009-04-15)
A novel algorithm implementing Chebyshev spectral collocation (pseudospectral) method in combination with Newton's method is proposed for the nonlinear two-point boundary value problem (BVP) arising in solving propagation equations in fiber Raman amplifier. Moreover, an algorithm to train the known linear solution for use as a starting solution for the Newton iteration is proposed and successfully implemented. The exponential accuracy obtained by the proposed Chebyshev pseudospectral method is demonstrated ...
A projection-based stabilized finite element method for steady-state natural convection problem
Çıbık, Aytekin; Kaya Merdan, Songül (Elsevier BV, 2011-9)
We formulate a projection-based stabilization finite element technique for solving steady-state natural convection problems. In particular, we consider heat transport through combined solid and fluid media. This stabilization does not act on the large flow structures. Based on the projection stabilization idea, finite element error analysis of the problem is investigated and optimal errors for the velocity, temperature and pressure are established. We also present some numerical tests which both verify the ...
A quadtree-based adaptively-refined cartesian-grid algorithm for solution of the euler equations
Bulkök, Murat; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2005)
A Cartesian method for solution of the steady two-dimensional Euler equations is produced. Dynamic data structures are used and both geometric and solution-based adaptations are applied. Solution adaptation is achieved through solution-based gradient information. The finite volume method is used with cell-centered approach. The solution is converged to a steady state by means of an approximate Riemann solver. Local time step is used for convergence acceleration. A multistage time stepping scheme is used to ...
A GPU-accelerated adaptive discontinuous Galerkin method for level set equation
KARAKUS, A.; WARBURTON, T.; AKSEL, MEHMET HALUK; Sert, Cüneyt (2016-01-02)
This paper presents a GPU-accelerated nodal discontinuous Galerkin method for the solution of two- and three-dimensional level set (LS) equation on unstructured adaptive meshes. Using adaptive mesh refinement, computations are localised mostly near the interface location to reduce the computational cost. Small global time step size resulting from the local adaptivity is avoided by local time-stepping based on a multi-rate Adams-Bashforth scheme. Platform independence of the solver is achieved with an extens...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations
Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01)
In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
Citation Formats
S. Kaya Merdan, “A Projection-Based VMS Method on Linearly Extrapolated BDF2Time-stepping Scheme for Navier-Stokes Equations,” 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/86608.