The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. In this work, a high-order Central Essentially Non-Oscillatory (CENO) finite-volume scheme is developed for the Euler and Navier-Stokes equations in three dimensions. The proposed CENO scheme is based on a hybrid solution reconstruction procedure using a fixed central stencil. A solution smoothness indicator facilitates the hybrid switching between a high-order k-exact reconstruction technique, and a monotonicity preserving limited piecewise linear reconstruction algorithm. The resulting scheme is applied to the compressible forms of the Euler and Navier-Stokes equations in three dimensions. The latter of which includes the application of this high-order work to the Large Eddy Simulation (LES) of turbulent non-reacting flows.

The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. In this work, a high-order Central Essentially Non-Oscillatory (CENO) finite-volume scheme is developed for the Euler and Navier-Stokes equations in three dimensions. The proposed CENO scheme is based on a hybrid solution reconstruction procedure using a fixed central stencil. A solution smoothness indicator facilitates the hybrid switching between a high-order k-exact reconstruction technique, and a monotonicity preserving limited piecewise linear reconstruction algorithm. The resulting scheme is applied to the compressible forms of the Euler and Navier-Stokes equations in three dimensions. The latter of which includes the application of this high-order work to the Large Eddy Simulation (LES) of turbulent non-reacting flows.

A 3d parallel CFD code is written to investigate the characteristics of and differences between Large Eddy Simulation (LES) models in the context of simulating a thermal buoyant plume. An efficient multigrid scheme is incorporated to solve the Poisson equation, resulting from the fractional step, projection method used to solve the Low Mach Number (LMN) Navier-Stokes equations. A wide range of LES models are implemented, including a variety of eddy models, structure models, mixed models and dynamic models, for both the momentum stresses and the temperature fluxes. Generalised gradient flux models are adapted from their RANS counterparts, and also tested. A number of characteristics are observed in the LES models relating to the thermal plume simulation in particular and turbulence in general. Effects on transition, dissipation, backscatter, equation balances, intermittency and energy spectra are all considered, as are the impact of the governing equations, the discretisation scheme, and the effect of grid coarsening. Also characteristics to particular models are considered, including the subgrid kinetic energy for the one-equation models, and constant histories for dynamic models. The argument that choice of LES model is unimportant is shown to be incorrect as a general statement, and a recommendation for when the models are best used is given.

Hydropower is a more environmental friendly way of producing electric power than many other alternatives today. Though, the effects of constructing mega dams are much tangible for the local eco systems in addition to changing many people’s lives forever. In order to prevent floods, riverbank erosions or landslides, proper investigations of the environmental impact from dam constructions must be performed. One of the key parameters in such investigations is the flow discharge velocity. This master thesis treats experimental measurements and numerical simulations of the velocity downstream a model of Xiluodu dam. The Xiluodu dam is a mega dam under construction in China and will have a total capacity of 12 600 MW when completed. The model is in scale 1:100 and the experiments have been performed at Department of Hydraulic Engineering, Tsinghua University, Beijing, China. The velocity profile shows that the velocity in the middle of the river is larger than the velocity at the surface and near the riverbank. The comparison between the measured and the simulated velocities shows a difference of less than 20 percent in almost all points which can be considered as a good result. In those points where the difference is more than 20 percent, this is believed to be due to the position of these points. Some of them were located near a vortex and others very close to the bottom. This is a problem when sparsely measured topography in combination with linear interpolation makes the boundaries of the simulations incorrect. In order to perform better simulations, more densely topography data and better flow boundary conditions should be used. More measuring points of the velocity could also improve the result.

This work develops a nonlinear, three-dimensional spectral collocation method for the simulation of the incompressible Navier-Stokes equations for geophysical and environmental flows. These flows are often driven by the interaction of stratified fluid with topography, which is accurately accounted for in this model using a mapped coordinate system. The spectral collocation method used here evaluates derivatives with a Fourier trigonometric or Chebyshev polynomial expansion as appropriate, and it evaluates the nonlinear terms directly on a collocated grid. The coordinate mapping renders ineffective fast solution methods that rely on separation of variables, so to avoid prohibitively expensive matrix solves this work develops a low-order finite-difference preconditioner for the implicit solution steps. This finite-difference preconditioner is itself too expensive to apply directly, so it is solved pproximately with a geometric multigrid method, using semicoarsening and line relaxation to ensure convergence with locally anisotropic grids. The model is discretized in time with a third-order method developed to allow variable timesteps. This multi-step method explicitly evaluates advective terms and implicitly evaluates pressure and viscous terms. The model’s accuracy is demonstrated with several test cases: growth rates of Kelvin-Helmholtz billows, the interaction of a translating dipole with no-slip boundaries, and the generation of internal waves via topographic interaction. These test cases also illustrate the model’s use from a high-level programming perspective. Additionally, the results of several large-scale simulations are discussed: the three-dimensional dipole/wall interaction, the evolution of internal waves with shear instabilities, and the stability of the bottom boundary layer beneath internal waves. Finally, possible future developments are discussed to extend the model’s capabilities and optimize its performance within the limits of the underlying numerical algorithms.

Recent increases in computing power and memory have created renewed interest in alternative grid schemes such as unstructured grids, which facilitate rapid grid generation by relaxing restrictions on grid structure. Three rotor models have been incorporated into a popular fixed-wing unstructured computational fluid dynamics (CFD) solver to increase its capability and facilitate availability to the rotorcraft community. The benefit of unstructured grid methods is demonstrated through rapid generation of high fidelity configuration models. The simplest rotor model is the steady state actuator disk approximation. By transforming the unsteady rotor problem into a steady state one, the actuator disk can provide rapid predictions of performance parameters such as lift and drag. The actuator blade and overset blade models provide a depiction of the unsteady rotor wake, but incur a larger computational cost than the actuator disk. The actuator blade model is convenient when the unsteady aerodynamic behavior needs to be investigated, but the computational cost of the overset approach is too large. The overset or chimera method allows the blades loads to be computed from first-principles and therefore provides the most accurate prediction of the rotor wake for the models investigated. The physics of the flow fields of these models for rotor/fuselage interaction are explored, along with efficiencies and limitations of each methodology.

In this thesis, the two-dimensional, transient, laminar flow of viscous and incompressible fluids is solved by using the dual reciprocity boundary element method (DRBEM). Natural convection and mixed convection flows are also solved with the addition of energy equation. Solutions of natural convection flow of nanofluids and micropolar fluids in enclosures are obtained for highly large values of Rayleigh number. The fundamental solution of Laplace equation is used for obtaining boundary element method (BEM) matrices whereas all the other terms in the differential equations governing the flows are considered as nonhomogeneity. This is the main advantage of DRBEM to tackle the nonlinearities in the equations with considerably small computational cost. All the convective terms are evaluated by using the DRBEM coordinate matrix which is already computed in the formulation of nonlinear terms. The resulting systems of initial value problems with respect to time are solved with forward and central differences using relaxation parameters, and the fourth-order Runge-Kutta method. The numerical stability analysis is developed for the flow problems considered with respect to the choice of the time step, relaxation parameters and problem constants. The stability analysis is made through an eigenvalue decomposition of the final coefficient matrix in the DRBEM discretized system. It is found that the implicit central difference time integration scheme with relaxation parameter value close to one, and quite large time steps gives numerically stable solutions for all flow problems solved in the thesis. One-and-two-sided lid-driven cavity flow, natural and mixed convection flows in cavities, natural convection flow of nanofluids and micropolar fluids in enclosures are solved with several geometric configurations. The solutions are visualized in terms of streamlines, vorticity, microrotation, pressure contours, isotherms and flow vectors to simulate the flow behaviour.

Richtmyer-Meshkov instability (RMI) occurs when an interface of two fluids with different densities is impulsively accelerated. The main interest in RMI is to understand the growth of perturbations, and numerous theoretical models have been developed and validated against experimental/numerical studies. However, most of the studies assume very simple initial conditions. Recently, more complex RMI has been studied, and this study focuses on two cases: reshocked RMI and multiphase RMI. It is well known that reshock to the species interface causes rapid growth of interface perturbation amplitude. However, the growth rates after reshock are not well understood, and there are no practical theoretical models yet due to its complex interface conditions at reshock. A couple of empirical expressions have been derived from experimental and numerical studies, but these models are limited to certain interface conditions. This study performs parametric numerical studies on various interface conditions, and the empirical models on the reshocked RMI are derived for each case. It is shown that the empirical models can be applied to a wide range of initial conditions by choosing appropriate values of the coefficient. The second part of the study analyzes the flow physics of multiphase RMI. The linear growth model for multiphase RMI is derived, and it is shown that the growth rates depend on two nondimensional parameters: the mass loading of the particles and the Stokes number. The model is compared to the numerical predictions under two types of conditions: a shock wave hitting (1) a perturbed species interface surrounded by particles, and (2) a perturbed particle cloud. In the first type of the problem, the growth rates obtained by the numerical simulations are in agreement with the multiphase RMI growth model when Stokes number is small. However, when the Stokes number is very large, the RMI motion follows the single-phase RMI growth model since the particle do not rapidly respond while the RMI instability grows. The second type of study also shows that the multiphase RMI model is applicable if Stokes number is small. Since the particles themselves characterize the interface, the range of applicable Stokes number is smaller than the first study. If the Stokes number is in the order of one or larger, the interface experiences continuous acceleration and shows the growth profile similar to a Rayleigh-Taylor instability.

The relative dispersion of one fluid particle with respect to another is fundamentally related to the transport and mixing of contaminant species in turbulent flows. The most basic consequence of Kolmogorov's 1941 similarity hypotheses for relative dispersion, the Richardson-Obukhov law that mean-square pair separation distance grows with the cube of time at intermediate times in the inertial subrange, is notoriously difficult to observe in the environment, laboratory, and direct numerical simulations (DNS). Inertial subrange scaling in size parameters like the mean-square pair separation requires careful adjustment for the initial conditions of the dispersion process as well as a very wide range of scales (high Reynolds number) in the flow being studied. However, the statistical evolution of the shapes of clusters of more than two particles has already exhibited statistical invariance at intermediate times in existing DNS. This invariance is identified with inertial-subrange scaling and is more readily observed than inertial-subrange scaling for seemingly simpler quantities such as the mean-square pair separation Results from dispersion of clusters of four particles (called tetrads) in large-scale DNS at grid resolutions up to 4096 points in each of three directions and Taylor-scale Reynolds numbers from 140 to 1000 are used to explore the question of statistical universality in measures of the size and shape of tetrahedra in homogeneous isotropic turbulence in distinct scaling regimes at very small times (ballistic), intermediate times (inertial) and very late times (diffusive). Derivatives of fractional powers of the mean-square pair separation with respect to time normalized by the characteristic time scale at the initial tetrad size constitute a powerful technique in isolating cubic time scaling in the mean-square pair separation. This technique is applied to the eigenvalues of a moment-of-inertia-like tensor formed from the separation vectors between particles in the tetrad. Estimates of the proportionality constant "g" in the Richardson-Obukhov law from DNS at a Taylor-scale Reynolds number of 1000 converge towards the value g=0.56 reported in previous studies. The exit time taken by a particle pair to first reach successively larger thresholds of fixed separation distance is also briefly discussed and found to have unexplained dependence on initial separation distance for negative moments, but good inertial range scaling for positive moments. The use of diffusion models of relative dispersion in the inertial subrange to connect mean exit time to "g" is also tested and briefly discussed in these simulations. Mean values and probability density functions of shape parameters including the triangle aspect ratio "w," tetrahedron volume-to-gyration radius ratio, and normalized moment-of-inertia eigenvalues are all found to approach invariant forms in the inertial subrange for a wider range of initial separations than size parameters such as mean-square gyration radius. These results constitute the clearest evidence to date that turbulence has a tendency to distort and elongate multiparticle configurations more severely in the inertial subrange than it does in the diffusive regime at asymptotically late time. Triangle statistics are found to be independent of initial shape for all time beyond the ballistic regime. The development and testing of different schemes for parallelizing the cubic spline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particles from processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.

Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 188-196).