Incompressible flow simulations using least squares spectral element method on adaptively refined triangular grids

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Tezin Türü: Yüksek Lisans

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

Tezin Onay Tarihi: 2012

Öğrenci: OSMAN AKDAĞ

Danışman: CÜNEYT SERT

Özet:

The main purpose of this study is to develop a flow solver that employs triangular grids to solve two-dimensional, viscous, laminar, steady, incompressible flows. The flow solver is based on Least Squares Spectral Element Method (LSSEM). It has p-type adaptive mesh refinement/coarsening capability and supports p-type nonconforming element interfaces. To validate the developed flow solver several benchmark problems are studied and successful results are obtained. The performances of two different triangular nodal distributions, namely Lobatto distribution and Fekete distribution, are compared in terms of accuracy and implementation complexity. Accuracies provided by triangular and quadrilateral grids of equal computational size are compared. Adaptive mesh refinement studies are conducted using three different error indicators, including a novel one based on elemental mass loss. Effect of modifying the least-squares functional by multiplying the continuity equation by a weight factor is investigated in regards to mass conservation.