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The averaged Navier‐Stokes and the k‐e turbulence model equations are used to simulate turbulent flows in some internal flow cases. The discrete equations are solved by different variations of Multigrid methods. These include both steady state as well as time dependent solvers. Locally refined grids can be added dynamically in all cases. The Multigrid schemes result in fast convergence rates, whereas local grid refinements allow improved accuracy with rational increase in problem size. The applications of the solver to a 3‐D (cold) furnace model and to the simulation of the flow in a wind tunnel past an object prove the efficiency of the Multigrid scheme with local grid refinement.

The purpose of this paper is to study the effect of a computational grid in computational fluid dynamics‐based mathematical modeling, focusing on but not limiting the attention to industrial‐scale boilers.

A full boiler model is used to show the difficulties related to judging iteration and discretization errors in boiler modeling. Then, a single jet is studied in detail to determine the proper degree of local grid refinement required in the vicinity of jets in the full boiler model. Both a nonreactive axisymmetric jet exhausting into a quiescent atmosphere and a reactive jet exhausting into a crossfiow are studied.

Over two million computational cells are required for the grid‐independent solution for a single jet. Local grid refinement is shown to be a good option for improving the results consistently without an excessive increase in the number of computational cells. Using relatively coarse grids of tetrahedral cells with a finite‐volume‐based solver may cause serious errors in results, typically by overpredicting the jet spreading rate and underpredicting the mean axial centerline velocity. Relatively coarse grids of hexahedral cells are less prone to error in a case where a jet exhausts into a quiescent atmosphere. However, their performance deteriorates when a crossfiow is introduced. As assumed, the differences in the predicted reaction rate and species concentrations are significant in the reactive case. It is confirmed that the standard k‐ε model tends to overpredict the axisymmetric jet spreading rate. The estimated inlet turbulence intensity is not among the most critical factors in modeling. Estimations of the axisymmetric jet centerline velocity from the analytical correlation may not coincide with the modeling results.

The error caused by the computational grid may easily dominate the errors caused by simplifying models used in industrial‐scale boiler modeling (turbulence, combustion, radiative heat transfer, etc.).

The present study deals with grid independency issues in industrial‐scale boiler modeling in a systematic and profound manner.

The numerical solution of the diffusion equation in VLSI process simulation leads to large systems of nonlinear equations which have to be solved at every time step. For this purpose, a multigrid (MG) algorithm with locally refined grids is constructed. It is demonstrated that the method used here yields typical MG algorithm convergence rates, and reduces the amount of work considerably. The local refinements are controlled by an estimation of the discretization error which is calculated within the nonlinear MG method (FAS) and requires no extra computational work.

We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is calculated only at the midpoints lying between the locations of the given values. As a consequence, these interpolants can be calculated very efficiently. They are then tested in a time‐dependent very large scale integration process simulation application.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or direct contact to potential drops using the finite integration technique (FIT).

The methodology of calculating low‐frequency electromagnetic fields within high‐resolution anatomy models using the FIT is extended by a local grid refinement scheme using a non‐matching‐grid formulation domain. Furthermore, distributed computing techniques are presented. Several numerical examples are analyzed using these techniques.

Numerical simulations of low‐frequency current density distributions may now be performed with a higher accuracy due to an increased local grid resolution in the areas of interest in the human body voxel models when using the presented techniques.

The local subgridding approach is introduced to reduce the number of unknowns in the very large‐scale linear algebraic systems of equations that have to be solved and thus to reduce the required computational time and memory resources. The use of distributed computation techniques such as, e.g. the use of a parallel solver package as PETSc follows the same goals.

In 1982, Smith and Hutton published comparative results of several different convection‐diffusion schemes applied to a specially devised test problem involving near‐discontinuities and strong streamline curvature. First‐order methods showed significant artificial diffusion, whereas higher‐order methods gave less smearing but had a tendency to overshoot and oscillate. Perhaps because unphysical oscillations are more obvious than unphysical smearing, the intervening period has seen a rise in popularity of low‐order artificially diffusive schemes, especially in the numerical heat‐transfer industry. This paper presents an alternative strategy of using non‐artificially diffusive higher‐order methods, while maintaining strictly monotonic transitions through the use of simple flux‐limiter constraints. Limited third‐order upwinding is usually found to be the most cost‐effective basic convection scheme. Tighter resolution of discontinuities can be obtained at little additional cost by using automatic adaptive stencil expansion to higher order in local regions, as needed.

Heat transfer due to natural convection inside a closed cavity must be modeled to include the effects of turbulence if the Rayleigh number is sufficiently large. This study assesses the performance of several commonly used numerical turbulence models such as k‐ε, Renormalized Group k‐ε and Reynolds stress model, in predicting heat transfer due to natural convection inside an air‐filled cubic cavity. The cavity is maintained at 307 K on one side and 300 K on the opposite side with a linear temperature variation between these values on the remaining walls. Two cases are considered, one in which the heated side is vertical, and the other in which it is inclined at 45° from the horizontal. Rayleigh numbers of 10⁷, 10⁸, 10⁹ and 10¹⁰ are considered. Results of the three turbulence models are compared to experimentally determined values or values from correlations. It was found that the standard k‐ε model was the most effective model in terms of accuracy and computational economy.

The purpose of the paper is to predict the aerodynamic performance of a complete scale model H-Darrieus vertical axis wind turbine (VAWT) with end plates at different operating conditions. This paper aims at understanding the flow physics around a model VAWT for three different tip speed ratios corresponding to three different flow regimes.

This study achieves a first three-dimensional hybrid lattice Boltzmann method/very large eddy simulation (LBM-VLES) model for a complete scaled model VAWT with end plates and mast using the solver PowerFLOW. The power curve predicted from the numerical simulations is compared with the experimental data collected at Erlangen University. This study highlights the complexity of the turbulent flow features that are seen at three different operational regimes of the turbine using instantaneous flow structures, mean velocity, pressure iso-contours, blade loading and skin friction plots.

The power curve predicted using the LBM-VLES approach and setup provides a good overall match with the experimental power curve, with the peak and drop after the operational point being captured. Variable turbulent flow structures are seen over the azimuthal revolution that depends on the tip speed ratio (TSR). Significant dynamic stall structures are seen in the upwind phase and at the end of the downwind phase of rotation in the deep stall regime. Strong blade wake interactions and turbulent flow structures are seen inside the rotor at higher TSRs.

The computational cost and time for such high-fidelity simulations using the LBM-VLES remains expensive. Each simulation requires around a week using supercomputing facilities. Further studies need to be performed to improve analytical VAWT models using inputs/calibration from high fidelity simulation databases. As a future work, the impact of turbulent and nonuniform inflow conditions that are more representative of a typical urban environment also needs to be investigated.

The LBM methodology is shown to be a reliable approach for VAWT power prediction. Dynamic stall and blade wake interactions reduce the aerodynamic performance of a VAWT. An ideal operation close to the peak of the power curve should be favored based on the local wind resource, as this point exhibits a smoother variation of forces improving operational performance. The 3D flow features also exhibit a significant wake asymmetry that could impact the optimal layout of VAWT clusters to increase their power density. The present work also highlights the importance of 3D simulations of the complete model including the support structures such as end plates and mast.

Accurate predictions of power performance for Darrieus VAWTs could help in better siting of wind turbines thus improving return of investment and reducing levelized cost of energy. It could promote the development of onsite electricity generation, especially for industrial sites/urban areas and renew interest for VAWT wind farms.

A first high-fidelity simulation of a complete VAWT with end plates and supporting structures has been performed using the LBM approach and compared with experimental data. The 3D flow physics has been analyzed at different operating regimes of the turbine. These physical insights and prediction capabilities of this approach could be useful for commercial VAWT manufacturers.

This paper aims to present a first step toward developing a comprehensive methodology for fully resolved numerical simulations of fusion deposition modeling (FDM).

A front-tracking/finite volume method previously developed for simulations of multiphase flows is extended to model the injection of hot polymer and its cooling down.

The accuracy and convergence properties of the new method are tested by grid refinement, and the method is shown to produce convergent solutions for the shape of the filament, the temperature distribution, contact area and reheat region when new filaments are deposited on top of previously laid down filaments.

The present paper focuses on modeling the fluid flow and the cooling. The modeling of solidification, volume changes and residual stresses will be described in Part II.

The ability to carry out fully resolved numerical simulations of the fusion deposition process is expected to help explore new deposition strategies and provide the “ground truth” for the development of reduced-order models.

The present paper is the first fully resolved simulation of the deposition in fusion filament modeling.