Hydraulic structures such as dykes and groynes are commonly used to help control river flows and reduce flood risk. The present research aims to develop an idealized model of the hydrodynamics in the vicinity of a large river bend, and the advection and mixing processes where groynes are located. In this study a curvilinear model of shallow water equations is applied to investigate chaotic advection of particles in a river bend similar in dimensions to a typical bend in the River Danube, Hungary. First, a curvilinear grid generator is developed based on Poisson-type elliptic partial differential equations. The grid generator is verified for benchmark tests concerning a circular domain and for distorted grids in a rectangular domain. It is found that multi-grid (MG) and conjugate gradient (CG) methods performed better computationally than successive over-relaxation (SOR) in generating the curvilinear grids. The open channel hydrodynamics are modelled using the shallow water equations (SWEs) derived by depth-averaging the continuity and Navier-Stokes momentum equations. Both Cartesian and curvilinear forms of the shallow water equations are presented. Both sets of equations are discretized spatially using finite differences and the solution marched forward in time using fourth-order Runge-Kutta scheme. The shallow water solvers are verified and validated for uniform flow in the rectangular channel, wind-induced set up in rectangular and circular basins, flow past a sidewall expansion, and Shallow flow in a rectangular channel with single groyne. A Lagrangian particle tracking model is used to predict the trajectories of tracer particles, and bilinear interpolation is used to provide a representation of the continuous flow field from discrete results. The particle tracking model is verified for trajectories in the flow field of a single free vortex and in the alternating flow field of a pair of blinking vortices. Excellent agreement is obtained with analytical solutions, previously published results in the literature. The combined shallow flow and Lagrangian particle tracking model is then used to simulate particle advection in the flow past a side-wall cavity containing a groyne and reasonable agreement is obtained with published experimental and alternative numerical data. Finally, the combined model is applied to simulate the shallow flow hydrodynamics, advection and mixing processes in the vicinity of groynes in river bend, the dimensions representative of a typical bend in the Danube River, Hungary.

This thesis present an efficient approach for performing smoke simulation on curvilinear grids. The solution of the Navier-Stokes equations on curvilinear is made on three steps: advection, pressure solving and velocity projection. The proposed advection method is simple, fast and unconditionally-stable. Our solution is able to maintain a staggered-grid variable arrangement, and includes an efficient solution to enforce mass conservation. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, lending to more realistic results, with just a small increment in computational cost. Moreover, we are able to condensate cells where interesting artifacts tend to appear, like swirling vortices or turbulence. We demonstrate the effectiveness of our approach, both in 2-D and 3-D, through a variety of high-quality smoke simulations and animations. These examples show the integration of our method with overlapping grids and multigrid techniques.

This thesis present an efficient approach for performing smoke simulation on curvilinear grids. The solution of the Navier-Stokes equations on curvilinear is made on three steps: advection, pressure solving and velocity projection. The proposed advection method is simple, fast and unconditionally-stable. Our solution is able to maintain a staggered-grid variable arrangement, and includes an efficient solution to enforce mass conservation. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, lending to more realistic results, with just a small increment in computational cost. Moreover, we are able to condensate cells where interesting artifacts tend to appear, like swirling vortices or turbulence. We demonstrate the effectiveness of our approach, both in 2-D and 3-D, through a variety of high-quality smoke simulations and animations. These examples show the integration of our method with overlapping grids and multigrid techniques.

This thesis present an efficient approach for performing smoke simulation on curvilinear grids. The solution of the Navier-Stokes equations on curvilinear is made on three steps: advection, pressure solving and velocity projection. The proposed advection method is simple, fast and unconditionally-stable. Our solution is able to maintain a staggered-grid variable arrangement, and includes an efficient solution to enforce mass conservation. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, lending to more realistic results, with just a small increment in computational cost. Moreover, we are able to condensate cells where interesting artifacts tend to appear, like swirling vortices or turbulence. We demonstrate the effectiveness of our approach, both in 2-D and 3-D, through a variety of high-quality smoke simulations and animations. These examples show the integration of our method with overlapping grids and multigrid techniques.

Space weather is the field within the space sciences that studies how the Earths magnetosphere is influenced by the Sun. The Sun is constantly emitting dangerous radiation and plasma which in some cases can affect or damage the systems on Earth. Scientists have an interest in studying this interaction and therefore visualizations of space weather data are useful. OpenSpace is an interactive software that visualizes the entire known universe with real-time data. OpenSpace supports a range of different visualization methods and techniques, for this work, the relevant visualization tools are field lines and cut planes. GAMERA is a simulation model that simulates a wide range of situations where plasma is subjected to the influence of magnetic fields, the simulations are based on curvilinear grids. This project focuses on implementing data from GAMERA into OpenSpace. OpenSpace already supports a variety of different simulation models, although none that uses curvilinear grids for the data. The curvilinear grid can adapt to the specific shape and geometry of the data, allowing for more accurate data representation. The project aims to create a pipeline for reading data files from simulation runs and visualize it as field lines and cut planes. The files used in this project contain data suitable for volumes and field lines. The method was to first develop a reader to extract and manage desired data from HDF5 files in which the simulation data is stored. The data used to visualize field lines is rendered with an already existing component in OpenSpace. Secondly, a slice operation was developed to extract cut planes from the files containing data for volume visualization, these are then visualized with the help of a component for rendering cut planes which was developed during this work. The work led to a pipeline that reads and manages simulation data from GAMERA and the data is successfully visualized. However, there is room for improvement in color rendering, robustness and level of user interaction during runtime. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>