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

Joint Inversion of Fracture Model Properties for CO2 Storage Monitoring or Oil Recovery History Matching

International audienceFor oil recovery or CO2 storage, "reservoirs" are commonly used to designate geological structures where oil can be found or CO2 can be stored. All reservoirs present a heterogeneity in terms of rock type and properties (such as porosity and permeability). In addition, some of these reservoirs present fractures and faults. Fractured reservoirs are an important part of the oil reserves in the world (Middle East, Gulf of Mexico, etc.) and some of them are important reservoirs in terms of oil volume and productivity in spite of the fractures. In addition, studies of reservoirs for geologic storage of CO2 have shown the existence of diffuse fractures and faults and their strong impacts on flow. A key point in fractured reservoirs is to understand the geometry and hydraulic conductivity of the network formed by the fractures. This requires the construction of a reservoir model that integrates all available conceptual knowledge and quantitative data. The topic of the present paper deals with a new methodology able to perform the history matching of a fractured reservoir model by adapting the sub-seismic fault properties and positions. The main difficulty of this work is to generate a sub-seismic fault network whose fault positions can be easily modified while respecting the statistical fault model. The sub-seismic fault model we have chosen allows us to obtain a sub-seismic fault network that is consistent with the seismic fault network and that succeeds in capturing the specific spatial organization of the faults. In a first step, the geometry of the seismic fault network is characterized using fractal methods. Sub-seismic faults are then generated according to a stochastic algorithm. Finally, the geometry of this discrete fracture network is optimized in order to match the hydrodynamic data about the reservoir. The optimization algorithm modifies the sub-seismic fault positions, leading to the history matching of the reservoir model. Fractal properties are preserved during the deformation process. These different steps are demonstrated on a realistic synthetic case

Three-Dimensional Navier-Stokes Simulation of Space Shuttle Main Propulsion 17-inch Disconnect Valves

A steady incompressible three-dimensional viscous flow analysis has been conducted for the Space Shuttle external tank/orbiter propellant feed line disconnect flapper valves with upstream elbows. The Navier-Stokes code, INS3D, is modified to handle interior obstacles and a simple turbulence model. The flow solver is tested for stability and convergence in the presence of interior flappers. An under-relaxation scheme has been incorporated to improve the solution stability. Important flow characteristics such as secondary flows, recirculation, vortex and wake regions, and separated flows are observed. Computed values for forces, moments, and pressure drop are in satisfactory agreement with water flow test data covering a maximum tube Reynolds number of 3.5 million. The predicted hydrodynamical stability of the flappers correlates well with the measurements

The Antares Collaboration : Contributions to the 34th International Cosmic Ray Conference (ICRC 2015, The Hague)

The ANTARES detector, completed in 2008, is the largest neutrino telescope in the Northern hemisphere. Located at a depth of 2.5 km in the Mediterranean Sea, 40 km off the Toulon shore, its main goal is the search for astrophysical high energy neutrinos. In this paper we collect the 21 contributions of the ANTARES collaboration to the 34th International Cosmic Ray Conference (ICRC 2015). The scientific output is very rich and the contributions included in these proceedings cover the main physics results, ranging from steady point sources, diffuse searches, multi-messenger analyses to exotic physics

1996 Coolant Flow Management Workshop

The following compilation of documents includes a list of the 66 attendees, a copy of the viewgraphs presented, and a summary of the discussions held after each session at the 1996 Coolant Flow Management Workshop held at the Ohio Aerospace Institute, adjacent to the NASA Lewis Research Center, Cleveland, Ohio on December 12-13, 1996. The workshop was organized by H. Joseph Gladden and Steven A. Hippensteele of NASA Lewis Research Center. Participants in this workshop included Coolant Flow Management team members from NASA Lewis, their support service contractors, the turbine engine companies, and the universities. The participants were involved with research projects, contracts and grants relating to: (1) details of turbine internal passages, (2) computational film cooling capabilities, and (3) the effects of heat transfer on both sides. The purpose of the workshop was to assemble the team members, along with others who work in gas turbine cooling research, to discuss needed research and recommend approaches that can be incorporated into the Center's Coolant Flow Management program. The workshop was divided into three sessions: (1) Internal Coolant Passage Presentations, (2) Film Cooling Presentations, and (3) Coolant Flow Integration and Optimization. Following each session there was a group discussion period

Efficient CAD based adjoint optimization of turbomachinery using adaptive shape parameterization

The present thesis incorporates the CAD model into an adjoint-based optimization loop and uses it for the shape optimization of a 2D transonic turbine blade mid-section (profile). This is demonstrated by performing a single and multipoint optimization of the LS89 turbine, originally designed at the VKI. Substantial aerodynamic improvements are reported for both design point and off-design conditions.The case is deeply analysed from the flow analysis point of view. The present thesis is a step forward in three main aspects. First, the way the CAD model (for turbomachinery applications) is used within the shape optimization loop.To include the CAD model into the optimization loop, the CAD kernel and the grid generator (multiblock structured) are differentiated using the Algorithmic Differentiation (AD) tool ADOL-C. The advantage of including the CAD model in the design system is that assembly or manufacturing constraints can be imposed on the shape, allowing the optimized model or component to be manufactured. Second, a new definition of the parametric effectiveness indicator is proposed, based on the ability of a set of CAD-based design variables to produce a shape change using the adjoint sensitivities. An interesting thing is that parametric effectiveness considers the design variables can be non-orthogonal to each other and it can be applied to any type of constrained or unconstrained problems. If, in the beginning of the optimization, the parametric effectiveness is high, it is expected to reach a final solution with increased performance. Third, a new adaptive shape parameterization strategy is adopted, which is assisted by the above parametric effectiveness indicator in order to explore the design space more efficiently. The parametric effectiveness, which rates the quality of a CAD based parameterization for optimization, is used in a novel multilevel shape refinement procedure to: (1) introduce the minimum amount of design variables required to modify the shape in the direction the adjoint sensitivities dictate; (2) to create the best parameterization to be used during the optimization. By using the proposed methods and tools, not only the optimal geometry is defined by the CAD, which is the industry adopted standard for the design of components, but also, the designer avoids the use of either too few (slow improvements from cycle to cycle) or too many (increase the computational burden) design variables. The proposed methodology results to be an effective strategy to explore rich design spaces, to improve convergence rate, robustness and final solution of the adjoint-based optimization.Aquesta tesi incorpora el model de CAD en un procés iteratiu d'optimització basat en el mètode adjunt i l'utilitza per a l'optimització de la secció d'una turbina transónica 2D (perfil). Això es demostra realitzant una optimització de punt únic i multipunt de la turbina LS89, originalment dissenyada en el VKI. Es reporten millores aerodinàmiques substancials tant per al punt de disseny com per les condicions fora del disseny. El cas s'analitza en profunditat des del punt de vista aerodinàmic. Aquesta tesi representa un avanç en tres aspectes principals. Primer, la forma en què es fa servir el model CAD (per a aplicacions de turbomàquines) dins el procés d'optimització. Per incloure el model CAD en el bucle d'optimització, s'apliquen tècniques de diferenciació algorítmica (l'eina ADOL-C) al kernel del CAD i el generador de la malla (estructurada i multibloc). L'avantatge d'incloure el model CAD en el sistema de disseny és que es poden imposar restriccions de fabricació a la geometria, i això permet que el disseny ja optimitzat es pugui fabricar. En segon lloc, es proposa una nova definició de l'indicador d'efectivitat paramètrica, basat en la capacitat de produir el canvi en la geometria que dicta el mètode adjunt mitjançant l'ús de les variables de disseny que defineixen el model CAD. Cal destacar que l'efectivitat paramètrica considera que les variables de disseny poden ser no ortogonals entre si i es pot aplicar a qualsevol tipus de problemes restringits o no restringits. Si, al començament de l'optimització, l'efectivitat paramètrica és alta, s'espera que l'optimització arribi a una solució final amb major rendiment. En tercer lloc, s'adopta una nova estratègia de parametrització adaptativa, que és assistida per l'indicador d'efectivitat paramètrica anterior per explorar l'espai de disseny de manera més eficient. L'efectivitat paramètrica, que classifica la qualitat d'una parametrització basada en CAD per a l'optimització, s'utilitza en un nou procediment de refinament multinivell per: (1) introduir la quantitat mínima de variables de disseny requerides per modificar la geometria en la direcció que dicten les sensibilitats del mètode adjunt; (2) per crear la millor parametrització que s'utilitzarà durant l'optimització. En utilitzar els mètodes i eines proposats, no només la geometria òptima està definida en el model CAD, que és l'estàndard adoptat per la indústria per al disseny de components, sinó que també el dissenyador evita l'ús de molt poques (millores lentes de cicle a cicle) o massa variables de disseny (augmenten la càrrega computacional). La metodologia proposada resulta ser una estratègia efectiva per explorar espais de disseny enriquits, millora la taxa de convergència, la solidesa i la solució final de l'optimització basada en el mètode adjunt