<p>An explicit algebraic Reynolds stress model (EARSM) based ona pressure strain rate model including terms tensoriallynonlinear in the mean velocity gradients is developed in orderto improve predictions for .ows with strong curvature and/orrotation. This work has been carried out in the context of acollaborative international project on high-lift aerodynamics.For 2D mean .ows the nonlinear terms can easily be accountedfor in the model formulation. This is not the case for 3D mean.ows and approximations making the 2D and 3D mean .owformulations consistent are suggested. The proposed EARSM, theparent-EARSM and the corresponding di.erential Reynolds stressmodels (DRSM) are tested for spanwise rotating channel .ow andaxially rotating pipe .ow. The model predictions are comparedto experimental and DNS data. The nonlinear extensions areshown to have a signi.cant e.ect on the .ow predictions,somewhat less pronounced for the DRSM though. The turbulentdi.usion modelling in the EARSM computations is important forthe rotating pipe. It is shown that by using a Daly and Harlowdi.usion model, turbulence levels in good agreement withexperiments and DRSM can be achieved. However, by using asimpler e.ective eddy viscosity based di.usion model theturbulence kinetic energy levels are drastically overpredicted.Finally the proposed EARSM is tested on a standard high-liftcon.guration. The EARSM predictions are compared withexperiments and the predictions made by the standard K - ωtwo-equation model.</p><p><b>Descriptors:</b>Turbulence model, nonlinear modelling,streamline curvature, high-lift aerodynamics.</p>

In the past few decades, many people spent a lot of time and used many different ways, which includes analytic method, numerical method, and experimental observations for investigating the flow around circular cylinder problem. Eventually, the purpose of these investigations is to determinate the force acting on the cylinder and which is very useful and important for marine and hydraulic engineering. Essentially, it can be divided into three circumstances, (i) the flow around a fixed cylinder, (ii) the flow around a rotating cylinder, (iii) the flow around a moving cylinder. The first two conditions have already been will discussed. Consequently, besides analyzing the first two conditions and comparing with reference papers, the purpose of this present is discussing the variation of the flow field and the force acting on the cylinder by using finite difference method. Because of the considerable quantity of computation, using parallel computing for this model to speedup the numerical process is also one of the issues of the present.

In this study, we apply the streamline-based production data integration method to condition a multimillion cell geologic model to historical production response for a giant Saudi Arabian reservoir. The field has been under peripheral water injection with 16 injectors and 70 producers. There is also a strong aquifer influx into the field. A total of 30 years of production history with detailed rate, infill well and re-perforation schedule were incorporated via multiple pressure updates during streamline simulation. Also, gravity and compressibility effects were included to account for water slumping and aquifer support. To our knowledge, this is the first and the largest such application of production data integration to geologic models accounting for realistic field conditions. We have developed novel techniques to analytically compute the sensitivities of the production response in the presence of gravity and changing field conditions. This makes our method computationally extremely efficient. The field application takes less than 6 hours to run on a PC. The geologic model derived after conditioning to production response was validated using field surveillance data. In particular, the flood front movement, the aquifer encroachment and bypassed oil locations obtained from the geologic model was found to be consistent with field observations. Finally, an examination of the permeability changes during production data integration revealed that most of these changes were aligned along the facies distribution, particularly the 'good' facies distribution with no resulting loss in geologic realism. We also propose a novel assisted history matching procedure for finite difference simulators using streamline derived sensitivity calculations. Unlike existing assisted history matching techniques where the user is required to manually adjust the parameters, this procedure combines the rigor of finite difference models and efficiencies of streamline simulators to perform history matching. Finite difference simulator is used to solve for pressure, flux and saturations which, in turn, are used as input for the streamline simulator for estimating the parameter sensitivities analytically. The streamline derived sensitivities are then used to update the reservoir model. The updated model is then used in the finite difference simulator in an iterative mode until a significant satisfactory history match is obtained. The assisted history matching procedure has been tested for both synthetic and field examples. The results show a significant speed-up in history matching using conventional finite difference simulators.

Two streamline, ordinary differential equation (ODE) models for detonation, the Chan-Kirby model and the straight streamline approach of Watt et al., are extended to a multiphase system of equations. These multiphase equations, with realistic equations of state, are used to better capture the heterogeneities in non-ideal explosives used in mining applications. Streamline ODE multidimensional models are normally obtained by reducing the partial differential equations (PDEs) describing the motion of the material to ODEs by making approximations about some of the physics of the problem. These models are referred to as reduced ODE models in this work and are the primary focus of this research into fast, efficient solutions of non-ideal explosives. In the development of these reduced order forms, some terms in the full equations have been removed for analytical convenience. Although this is not always the result of a formal order of magnitude analysis, this somewhat empirical approach is justified by simulation studies. In particular, by demonstrating that in a variety of benchmark problems, the reduced order ODEs give similar results to those obtained from the much more complex, full order PDE models. Further support is obtained by comparing the reduced order solution with experimental results. Comparisons with multiphase direct numerical simulations and experiments are undertaken to investigate the effect of the approximations and assumptions made in the derivation of the models. Both models produce comparable diameter effect curves for two different non-ideal explosives, EM120D and ANFO, in unconfined conditions. Empirical assumptions in the Chan-Kirby model can be eliminated but investigation shows that the straight streamline multiphase extension is based on better approximations for non-ideal explosives. This latter approach also gives better prediction of the diameter effect curve and detonation driving zone shape. The multiphase straight streamline model is then extended to model confined multiphase detonations, with realistic equations of state for the confining material, and predicts most strong confinement examples well. Future work of extending to curved streamlines and including confinement other than strong or weak is discussed.

An explicit algebraic Reynolds stress model (EARSM) based ona pressure strain rate model including terms tensoriallynonlinear in the mean velocity gradients is developed in orderto improve predictions for .ows with strong curvature and/orrotation. This work has been carried out in the context of acollaborative international project on high-lift aerodynamics.For 2D mean .ows the nonlinear terms can easily be accountedfor in the model formulation. This is not the case for 3D mean.ows and approximations making the 2D and 3D mean .owformulations consistent are suggested. The proposed EARSM, theparent-EARSM and the corresponding di.erential Reynolds stressmodels (DRSM) are tested for spanwise rotating channel .ow andaxially rotating pipe .ow. The model predictions are comparedto experimental and DNS data. The nonlinear extensions areshown to have a signi.cant e.ect on the .ow predictions,somewhat less pronounced for the DRSM though. The turbulentdi.usion modelling in the EARSM computations is important forthe rotating pipe. It is shown that by using a Daly and Harlowdi.usion model, turbulence levels in good agreement withexperiments and DRSM can be achieved. However, by using asimpler e.ective eddy viscosity based di.usion model theturbulence kinetic energy levels are drastically overpredicted.Finally the proposed EARSM is tested on a standard high-liftcon.guration. The EARSM predictions are compared withexperiments and the predictions made by the standard K - ωtwo-equation model. Descriptors:Turbulence model, nonlinear modelling,streamline curvature, high-lift aerodynamics.

No description available.

No description available.

No description available.

No description available.

Visualization of trivariate functions and vector fields with three components in scientific computation is still a hard problem in compute graphic area. People build their own visualization packages for their special purposes. And there exist some general-purpose packages (MatLab, Vis5D), but they all require extensive user experience on setting all the parameters in order to generate images. We present a simple package to produce simplified but productive images of 3-D vector fields. We used this method to render the magnetic field and current as solutions of the Ginzburg-Landau equations on a 3-D domain.