The aim of the thesis is to develop and validate subgrid-scale models that are relevant for large eddy simulations of complex flows including scalar mixing. A stochastic Smagorinsky model with adjustable variance and time scale is developed by adding a stochastic component to the Smagorinsky constant. The stochastic model is shown to provide for backscatter of both kinetic energy and scalar variance without causing numerical instabilities. In addition, new models for the subgrid-scale stress and passive scalar flux are derived from modelled subgrid scale transport equations. These models properly account for the anisotropy of the subgrid scales and have potentials wall bounded flows. The proposed models are validated in wall bounded flows with and without rotation and show potential or significantly improve predictions for such cases. / <p>QC 20100826</p>

A novel computational approach, Two Level Simulation (TLS), was developed based on the explicit reconstruction of the small-scale velocity by solving the small-scale governing equations on the domain with reduced dimension representing a collection of one-dimensional lines embedded in the three-dimensional flow domain. A coupled system of equations, that is not based on an eddy-viscosity hypothesis, was derived based on the decomposition of flow variables into the large-scale and the small-scale components without introducing the concept of filtering. Simplified treatment of the small-scale equations was proposed based on modeling of the small-scale advective derivatives and the small-scale dissipative terms in the directions orthogonal to the lines. TLS approach was tested to simulate benchmark cases of turbulent flows, including forced isotropic turbulence, mixing layers and well-developed channel flow, and demonstrated good capabilities to capture turbulent flow features using relatively coarse grids.

<p>The aim of the present study is to develop subgrid-scale models that are relevant for complex flows and combustion. A stochastic model based on a stochastic Smagorinsky constant with adjustable variance and time scale is proposed. The stochastic model is shown to provide for backscatter of both kinetic energy and scalar variance without causing numerical instabilities. A new subgrid-scale scalar flux model is developed using the same kind of methodology that leads to the explicit algebraic scalar flux model, EASFM, for RANS. The new model predicts the anisotropy of the subgrid-scales in a more realistic way than the eddy diffusion model. Both new models were tested in rotating homogeneous shear flow with a passive scalar. Rogallo’s method of moving the frame with the mean flow to enable periodic boundary conditions was used to simulate homogeneous shear flow.</p>

This thesis examines the importance of energy and momentum consistency in subgrid-scale parameterization for climate models. It is divided into two parts according to the two aspects of the problem that are investigated, namely the importance of momentum conservation alone and the consistency between energy and momentum conservation. The first part addresses the importance of momentum conservation alone. Using a zonally-symmetric model, it is shown that violating momentum conservation in the parameterization of gravity wave drag leads to large errors and non-robustness of the response to an imposed radiative perturbation in the middle atmosphere. Using the Canadian Middle Atmosphere Model, a three-dimensional climate model, it is shown that violating momentum conservation, by allowing gravity wave momentum flux to escape through the model lid, leads to large errors in the mean climate when the model lid is placed at 10 hPa. When the model lid is placed at 0.001 hPa the errors due to nonconservation are minimal. When the 10 hPa climate is perturbed by idealized ozone depletion in the southern hemisphere, nonconservation is found to significantly alter the polar temperature and surface responses. Overall, momentum conservation ensures a better agreement between the 10 hPa and the 0.001 hPa climates. The second part addresses the self-consistency of energy and momentum conservation. Using Hamiltonian geophysical fluid dynamics, pseudoenergy and pseudomomentum wave-activity conservation laws are derived for the subgrid-scale dynamics. Noether’s theorem is used to derive a relationship between the wave-activity fluxes, which represents a generalization of the first Eliassen-Palm theorem. Using multiple scale asymptotics a theoretical framework for subgrid-scale parameterization is built which consistently conserves both energy and momentum and respects the second law of thermodynamics. The framework couples a hydrostatic resolved-scale flow to a non-hydrostatic subgrid-scale flow. The transfers of energy and momentum between the two scales are understood using the subgrid-scale wave-activity conservation laws, whose relationships with the resolved-scale dynamics represent generalized non-acceleration theorems. The derived relationship between the wave-activity fluxes — which represents a generalization of the second Eliassen-Palm theorem — is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

This thesis examines the importance of energy and momentum consistency in subgrid-scale parameterization for climate models. It is divided into two parts according to the two aspects of the problem that are investigated, namely the importance of momentum conservation alone and the consistency between energy and momentum conservation. The first part addresses the importance of momentum conservation alone. Using a zonally-symmetric model, it is shown that violating momentum conservation in the parameterization of gravity wave drag leads to large errors and non-robustness of the response to an imposed radiative perturbation in the middle atmosphere. Using the Canadian Middle Atmosphere Model, a three-dimensional climate model, it is shown that violating momentum conservation, by allowing gravity wave momentum flux to escape through the model lid, leads to large errors in the mean climate when the model lid is placed at 10 hPa. When the model lid is placed at 0.001 hPa the errors due to nonconservation are minimal. When the 10 hPa climate is perturbed by idealized ozone depletion in the southern hemisphere, nonconservation is found to significantly alter the polar temperature and surface responses. Overall, momentum conservation ensures a better agreement between the 10 hPa and the 0.001 hPa climates. The second part addresses the self-consistency of energy and momentum conservation. Using Hamiltonian geophysical fluid dynamics, pseudoenergy and pseudomomentum wave-activity conservation laws are derived for the subgrid-scale dynamics. Noether’s theorem is used to derive a relationship between the wave-activity fluxes, which represents a generalization of the first Eliassen-Palm theorem. Using multiple scale asymptotics a theoretical framework for subgrid-scale parameterization is built which consistently conserves both energy and momentum and respects the second law of thermodynamics. The framework couples a hydrostatic resolved-scale flow to a non-hydrostatic subgrid-scale flow. The transfers of energy and momentum between the two scales are understood using the subgrid-scale wave-activity conservation laws, whose relationships with the resolved-scale dynamics represent generalized non-acceleration theorems. The derived relationship between the wave-activity fluxes — which represents a generalization of the second Eliassen-Palm theorem — is key to ensuring consistency between energy and momentum conservation. The framework includes a consistent formulation of heating and entropy production due to kinetic energy dissipation.

Solving the Navier-Stokes equations using direct numerical simulation (DNS) is computationally impractical, especially at high Reynolds numbers. Recent technological advances in supercomputing have paved the way for Large Eddy Simulations (LES) to circumvent this problem by resolving large scale turbulence motions and modeling only the small (subgrid) scales. However, LES modeling still requires advanced knowledge of the turbulence and LES models are currently very simplistic. Because of this, there has been considerable interest in hybrid turbulence models, which can perform either Reynolds Averaged Navier-Stokes (RANS) modeling or Large Eddy Simulation (LES). The self-adapting model presented is fundamentally different from prior LES models and these current hybrid models in that it achieves a completely natural evolution from RANS to LES to (with enough mesh resolution) DNS. A modified k/e model and a Reynolds stress transport model is implemented in this manner and is compared to DNS data of isotropic decaying turbulence. The results indicate that this modeling approach is practical and efficient. In addition, this approach is extensible and not restricted to a particular (RANS) transport equation.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23852号 / 工博第4939号 / 新制||工||1771(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 森 信人, 教授 平石 哲也, 准教授 志村 智也 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

There are two big challenges which restrict the extensive application of fully coupled geomechanics-reservoir modeling. The first challenge is computational effort. Consider a 3-D simulation combining pressure and heat diffusion, elastoplastic mechanical response, and saturation changes; each node has at least 5 degrees of freedom, each leading to a separate equation. Furthermore, regions of large p, T and σ′ gradients require small-scale discretization for accurate solutions, greatly increasing the number of equations. When the rock mass surrounding the reservoir region is included, it is represented by many elements or nodes. These factors mean that accurate analysis of realistic 3-D problems is challenging, and will so remain as we seek to solve larger and larger coupled problems involving nonlinear responses. To overcome the first challenge, the displacement discontinuity method is introduced wherein a large-scale 3-D case is divided into a reservoir region where Δp, ΔT and non-linear effects are critical and analyzed using FEM, and an outside region in which the reservoir is encased where Δp and ΔT effects are inconsequential and the rock may be treated as elastic, analyzed with a 3D displacement discontinuity formulation. This scheme leads to a tremendous reduction in the degrees of freedom, yet allows for reasonably rigorous incorporation of the reactions of the surrounding rock. The second challenge arises from some forms of numerical instability. There are actually two types of sharp gradients implied in the transient advection-diffusion problem: one is caused by the high Peclet numbers, the other by the sharp gradient which appears during the small time steps due to the transient solution. The way to eliminate the spurious oscillations is different when the sharp gradients are induced by the transient evolution than when they are produced by the advective terms, and existing literature focuses mainly on eliminating the spurious spatial temperature oscillations caused by advection-dominated flow. To overcome the second challenge, numerical instability sources are addressed by introducing a new stabilized finite element method, the subgrid scale/gradient subgrid scale (SGS/GSGS) method.

There are two big challenges which restrict the extensive application of fully coupled geomechanics-reservoir modeling. The first challenge is computational effort. Consider a 3-D simulation combining pressure and heat diffusion, elastoplastic mechanical response, and saturation changes; each node has at least 5 degrees of freedom, each leading to a separate equation. Furthermore, regions of large p, T and σ′ gradients require small-scale discretization for accurate solutions, greatly increasing the number of equations. When the rock mass surrounding the reservoir region is included, it is represented by many elements or nodes. These factors mean that accurate analysis of realistic 3-D problems is challenging, and will so remain as we seek to solve larger and larger coupled problems involving nonlinear responses. To overcome the first challenge, the displacement discontinuity method is introduced wherein a large-scale 3-D case is divided into a reservoir region where Δp, ΔT and non-linear effects are critical and analyzed using FEM, and an outside region in which the reservoir is encased where Δp and ΔT effects are inconsequential and the rock may be treated as elastic, analyzed with a 3D displacement discontinuity formulation. This scheme leads to a tremendous reduction in the degrees of freedom, yet allows for reasonably rigorous incorporation of the reactions of the surrounding rock. The second challenge arises from some forms of numerical instability. There are actually two types of sharp gradients implied in the transient advection-diffusion problem: one is caused by the high Peclet numbers, the other by the sharp gradient which appears during the small time steps due to the transient solution. The way to eliminate the spurious oscillations is different when the sharp gradients are induced by the transient evolution than when they are produced by the advective terms, and existing literature focuses mainly on eliminating the spurious spatial temperature oscillations caused by advection-dominated flow. To overcome the second challenge, numerical instability sources are addressed by introducing a new stabilized finite element method, the subgrid scale/gradient subgrid scale (SGS/GSGS) method.

A low-order discrete dynamical system (DDS) for finite-rate chemistry of H2-air combustion is derived in 3D. Fourier series with a single wavevector are employed to represent dependent variables of subgrid-scale (SGS) behaviors for applications to large-eddy simulation (LES). A Galerkin approximation is applied to the governing equations for comprising the DDS. Regime maps are employed to aid qualitative determination of useful values for bifurcation parameters of the DDS. Both isotropic and anisotropic assumptions are employed when constructing regime maps and studying bifurcation parameters sequences. For H2-air reactions, two reduced chemical mechanisms are studied via the DDS. As input to the DDS, physical quantities from experimental turbulent flow are used. Numerical solutions consisting of time series of velocities, species mass fractions, temperature, and the sum of mass fractions are analyzed. Numerical solutions are compared with experimental data at selected spatial locations within the experimental flame to check whether this model is suitable for an entire flame field. The comparisons show the DDS can mimic turbulent combustion behaviors in a qualitative sense, and the time-averaged computed results of some species are quantitatively close to experimental data.