A common alternative to full resolution of the near-wall region in computational fluid dynamics (CFD) simulations is the use of wall functions that decrease the mesh requirements in this region. This study presents two alternatives to current wall functions. The first method is based on numerically approximating a turbulent velocity profile using a one-dimensional subgrid contained within walljacent control cells. The second method is an analytical approach similar to previous wall function methods, but this method is valid both inside and outside of the fluid boundary layer. Use of both methods allows approximation of boundary layers of varying height relative to the first layer sizing. Use of these methods allows wall adjacent primary grid sizes to vary from low-Re model sizing of y+ ≈ 1 to grid sizes of y+ ~ 1000 or more without significant loss in accuracy, and with computational costs similar to currently used wall functions.

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.

The finite-difference time-domain (FDTD) method has been widely and effectively used for analysis in many kinds of electromagnetic problems. Generally, the computational space can be divided into many lattices with rectangular; and the length on each of these meshs is equivalent in unitary aspect. In some of those problems, a greatly improved accuracy of the solution can be obtained if a finer discretization is used in specific regions of the computational space. There are limitations of the present form of uniform FDTD. It must increase the computational cost (memory and CPU time). Concerning the impression, we are trying to find more efficient ways of utilizing nonuniform grids. Coarser mesh for uncomplicated structure and finer mesh for complicated structure in nonuniform grids. However, this way can use in part of cutting area only. There are two edges connects the truncation of computational space. A similar scheme has been used with nonuniform FDTD method by a modification to the mesh scheme. The subcell method is a very general approach, capable of analyzing arbitrarily-shaped structures. In local area the mesh change from rectangular to irregular. Subgridding method is dissimilar to the both methods. Furthermore, the anisotropic PML to decrease the electromagnetic wave from nonuniform mesh of the computational space. It have replaced Mur¡¦s first-order absorbing boundary conditions and Berenger¡¦s PML for improving computationally efficient. Finally, compare them with the anisotropic PML in the essay.

<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>

The research network “Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models” was organized with European funding (COST Action ES0905) for the period of 2010–2014. Its extensive brainstorming suggests how the subgrid-scale parameterization problem in atmospheric modeling, especially for convection, can be examined and developed from the point of view of a robust theoretical basis. Our main cautions are current emphasis on massive observational data analyses and process studies. The closure and the entrainment–detrainment problems are identified as the two highest priorities for convection parameterization under the mass–flux formulation. The need for a drastic change of the current European research culture as concerns policies and funding in order not to further deplete the visions of the European researchers focusing on those basic issues is emphasized.

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.

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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.

Detailed sensitivity numerical studies have shown that the mesh cell-size may have a drastic effect on the modelling of circulating fluidized bed with small particles. Typically, the cell-size must be of the order of few particle diameters to predict accurately the dynamical behaviour of a fluidized bed. Hence, the Euler-Euler numerical simulations of industrial processes are generally performed with grids too coarse to allow the prediction of the local segregation effects. Appropriate modelling, which takes into account the influence of unresolved structures, have been already proposed for monodisperse simulations. In this work, the influence of unresolved structures on a binary mixture of particles is investigated and models are proposed to account for those effect on bidisperse simulations of bidisperse gas-solid fluidized bed. To achieve this goal, Euler-Euler reference simulations are performed with grid refinement up to reach a mesh independent solution. Such kind of numerical simulation is very expensive and is restricted to very simple configurations. In this work, the configuration consists of a 3D periodical circulating fluidized bed, that could represent the established zone of an industrial circulating fluidized bed. In parallel, a filtered approach is developed where the unknown terms, called sub-grid contributions, appear. They correspond to the difference between filtered terms, which are calculated with the reference results then filtered, and resolved contributions, calculated with the filtered fields. Then spatial filters can be applied to reference simulation results to measure each sub-grid contribution appearing in the theoretical filtered approach. A budget analysis is carried out to understand and model the sub-grid term. The analysis of the filtered momentum equation shows that the resolved fluid-particle drag and inter-particle collision are overestimating the momentum transfer effects. The analysis of the budget of the filtered random kinetic energy shows that the resolved production by the mean shear and by the mean particle relative motion are underestimating the filtered ones. Functional models are proposed for the subgrid contributions of the drag and the inter-particle collision.