Spectral (h-p) element methods approach to the solution of poisson and helmholtz equations using matlab

---

Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Makina Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2006

Öğrenci: TUĞRUL MARAL

Eş Danışman: İLKER TARI, CÜNEYT SERT

Özet:

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.