Isogeometric analysis of depth averaged flow and contaminant transport equations in meandering open channels
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Date
2017
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Universiti Teknologi Malaysia
Abstract
This thesis brings together the fields of river engineering, specifically the nature of river mixing, and Iso-Geometric Analysis (IGA) as a computational method for solving solute transport problems. River mixing is studied using the depth averaged advection dispersion equation which requires velocity profile input. Initially, the flow equations are solved to determine the concentration in meandering channels by substituting the velocity profile into the governing equation to derive the dispersion coefficients. Unlike the conventional Finite Element Analysis (FEA), IGA adopts higher-order and higher-continuity discretization methods in the formulation, hence offers rich options in geometry modeling. The aim of this study is to employ IGA for improving the accuracy of Finite Element Method (FEM) and the stability of solution scheme by applying Streamwise Upwind Petrov Galerkin (SUPG), besides improving the finite element spaces using Non-uniform Rational Basis Spline (NURBS) basis functions. This study started with the investigation on the pros and cons of existing models for river mixing problems, followed by the building blocks of IGA. The modeling results showed that in determining the concentration in meandering channels, the tracer cloud behaves differently in these channels where the tracer cloud is almost symmetrical when entering the first bend. At the first bend apex, the tracer cloud separates into two parts due to the combined action of the secondary current and non-uniform primary flow. Subsequently, application of the method to a 9km2 catchment of Karun River in Iran implies that the IGA of depth averaged flow equations exhibits a cascade of velocity distribution as well as water elevation in the meandering channel. Despite the difficulties in applying the equations in the field, the proposed IGA is able to predict the flow characteristics on coarse discretization processes with accurate representation of the geometry. In addition, numerical tests of adopting IGA to improve the FEA accuracy suggest that the proposed methodology is able to simulate the river mixing behavior well, and yields higher per-degree-of-freedom accuracy. It was achieved through higher-order and higher-continuity isogeometric discretizations for the computation of flow in shallow river bends
Description
Thesis (PhD. (Civil Engineering))
Keywords
Meandering rivers, River engineering, Isogeometric analysis