Developments and trends in three-dimensional mesh generation

An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation

Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Application of Advanced Grid Generation Techniques for Flow Field Computations About Complex Configurations

In the computation of flow fields about complex configurations, it is very difficult to construct a boundary-fitted coordinate system. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach, and its applications are investigated in this study. The method is a conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-stage Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Steady state solutions of the Euler equations are presented and discussed. The solutions include: low speed flow over a sphere, high speed flow over a slender body, supersonic flows over a Butler-Wing at various Mach numbers and angles of attack, supersonic flow through a duct, and supersonic internal/external flow interaction for an aircraft configuration at various angles of attack. The results demonstrate that the multiple grids approach along with the conservative interfacing is capable of computing the flows about the complex configurations where the use of a single grid is not possible

Computational Fluid Dynamics Analysis of Two Savonius-Type Ocean Current Turbines with Augmentation Techniques

Ocean current turbines are one of many environmentally friendly, prospective energy sources out there, however, it is still at an embryonic stage in development. This thesis aims to build on the existing knowledge in the field, by investigating the design of two Savonius type ocean current turbines, both with- and without surrounding structures that augment their performances. The two profiles evaluated were the semi circular- and the elliptic blade profile. For this purpose, the computational fluid dynamics software, OpenFOAM, was utilised, with the geometry and mesh created in \textsc{Solidworks} and Gmsh, respectively. The Reynolds Average Navier-Stokes equations were used, employing the $k-\omega$ SST turbulence closure model, together with the PIMPLE pressure-velocity coupling algorithm. Wall functions were implemented to estimate the flow parameters in the wall boundaries, using an average $y^+$ value of 300. However, results show that this approach provided inaccurate results, most likely due to poor estimations of flow separation. Augmentations increased the power coefficient of the semi circular turbine by 50.78\%, from 0.258 to 0.389, whereas the elliptic profile saw a 79.71\% increase in power coefficient, from 0.276 to 0.496. Future work regarding this thesis should look at further enhancement of the elliptic profile, optimizing the augmentation around it. Moreover, a finer grid should be implemented

Geometry acquisition and grid generation: Recent experiences with complex aircraft configurations

Important issues involved in working with complex geometries are discussed. Approaches taken to address complex geometry issues in the McDonnell Aircraft Computational Grid System and related geometry processing tools are discussed. The efficiency of acquiring a suitable geometry definition, the need to manipulate the geometry, and the time and skill level required to generate the grid while preserving geometric fidelity are discussed

Numerical Methods for Neutron Transport Calculations of Nuclear Reactors

The objective of this thesis, which in clearly inspired by an industrial framework, is to try and narrow the gap between theoretical neutron modelling and application in the context of nuclear reactor design. This thesis is divided into three main chapters, preceded by a general overview. This structure reflects the three main topics which were chosen for this research project. The first topic develops the Spectral Element Method (SEM) approach and its use in conjunction with transport approximations. As it is documented in the specialized numerical analysis handbooks and in previous works by the author, the method has an excellent convergence rate which outperforms most classical schemes, but it has also some important drawbacks which sometimes seem to discourage its use for linear transport problems applied to nontrivial benchmarks. In order to elaborate the methodology of the specific problems encountered in reactor physics, three aspects are addressed looking for improvements. The first topic analyzed is related to the convergence order, whose value is less straightforward to define a priori by means of functional analysis than other numerical schemes. The adjective “spectral” refers in fact to the maximum order claimed, exponential with respect to the average size of the mesh. A comprehensive set of convergence tests is carried out applying SEM to a few transport models and with the aid of manufactured solutions, thus isolating the numerical effects from the deviations which are due only to modelling approximations. The hypothesis of grid conformity is also relaxed, replacing the classical Galerkin variational formulation with the Discontinuous Galerkin theory, characterized by a more flexible treatment of the mesh interfaces; this scheme allows local grid refinement and opens the way, in perspective, to mesh adaption. Finally, a simple and sufficiently flexible technique to deform the boundaries of each mesh is introduced and applied, in order to adapt the grid to curved geometries. In this way, the advantages of SEM can be applied to a vast class of common problems like lattice calculations. Moreover, thanks to a change of the basis functions used in SEM, it is possible to obtain elements with three sides (straight or deformed), that are a typical war horse of the Finite Element approach. The second topic is essentially devoted to the most “industrial” part of the thesis, developed entirely during the stay of the author in the AREVA NP headquarters in Paris. In AREVA, and in all other nuclear engineering enterprises, neutron diffusion is still the preferred neutronic model for full-core studies. Better approximations are reserved for library preparation, fuel studies and code validation, none of these being typically too much time or budget-constrained. Today needs start to require a certain level of improvement also in full-core analyses, trying to fitly model localized dis-homogeneities and reduce the penalizing engineering margins which are taken as provisions. On the other hand, a change in the model does not mean only an effort to write a new code, but has huge follow-ups due to the validation processes required by the authorities. Second-order transport may support the foreseen methodology update because it can be implemented re-using diffusion routines as the computational engine. The AN method, a second-order approximation of the transport equation, has been introduced in some studies, and its effect is discussed. Moreover, some effort has been reserved to the introduction of linear anisotropy in the model. The last topic deals with ray effects; they are a known issue of the discrete ordinate approach (SN methods) which is responsible for a reduction in the accuracy of the solution, especially in penetration problems with low scattering, like several shielding calculations performed for operator safety concerns. Ray effects are here characterized from a formal point of view in both static and time dependent situations. Then, quantitative indicators are defined to help with the interpretation of the SN results. Based on these studies, some mitigation measures are proposed and their efficacy is discussed