Spectral (h-p) element methods approach to the solution of Poisson and Helmholtz equations using Matlab

Download

index.pdf

Date

2006

Author

Maral, Tuğrul

Metadata

Show full item record

Item Usage Stats

142
views

69
downloads

A spectral element solver program using MATLAB is written for the solution of Poisson and Helmholtz equations. The accuracy of spectral methods (p-type high order) and the geometric flexibility of the low-order h-type finite elements are combined in spectral element methods. Rectangular elements are used to solve Poisson and Helmholtz equations with Dirichlet and Neumann boundary conditions which are homogeneous or non homogeneous. Robin (mixed) boundary conditions are also implemented. Poisson equation is also solved by discretising the domain with curvilinear quadrilateral elements so that the accuracy of both isoparametric quadrilateral and rectangular element stiffness matrices and element mass matrices are tested. Quadrilateral elements are used to obtain the stream functions of the inviscid flow around a cylinder problem. Nonhomogeneous Neumann boundary conditions are imposed to the quadrilateral element stiffness matrix to solve the velocity potentials.

Subject Keywords

Numerical Analysis., Mechanical Engineering.

URI

http://etd.lib.metu.edu.tr/upload/3/12607945/index.pdf
https://hdl.handle.net/11511/16114

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

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.
Inverse Sturm-Liouville Systems over the whole Real Line Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010) In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...
Solution of helmholtz type equations by differential quadrature method Kuruş, Gülay; Tezer, Münevver; Department of Mathematics (2004) This thesis presents the Differential Quadrature Method (DQM) for solving Helmholtz, modified Helmholtz and Helmholtz eigenvalue-eigenvector equations. The equations are discretized by using Polynomial-based and Fourier-based differential quadrature technique wich use basically polynomial interpolation for the solution of differential equation.
Implementation of different flux evaluation schemes into a two-dimensional Euler solver Eraslan, Elvan; Aksel, Mehmet Haluk; Department of Mechanical Engineering (2006) This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe’s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruc...
Geometric integrators for coupled nonlinear Schrödinger equation Aydın, Ayhan; Karasözen, Bülent; Department of Mathematics (2005) Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrödinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is d...

Citation Formats

T. Maral, “Spectral (h-p) element methods approach to the solution of Poisson and Helmholtz equations using Matlab,” M.S. - Master of Science, Middle East Technical University, 2006.