On adomian based numerical schemes for euler and navier-stokes equations, and application to aeroacoustic propagation

140 p.En esta tesis se ha desarrollado un nuevo método de integración en tiempo de tipo derivadas sucesivas (multiderivative), llamado ABS y basado en el algoritmo de Adomian. Su motivación radica en la reducción del coste de simulación para problemas en aeroacústica, muy costosos por su naturaleza transitoria y requisitos de alta precisión. El método ha sido satisfactoriamente empleado en ambas partes de un sistema híbrido, donde se distinguen la parte aerodinámica y la acústica.En la parte aerodinámica las ecuaciones de Navier-Stokes incompresibles son resueltas con unmétodo de proyección clásico. Sin embargo, la fase de predicción de velocidad ha sido modificadapara incluir el método ABS en combinación con dos métodos: una discretización espacial MAC devolúmenes finitos, y también con un método de alto orden basado en ADER. El método se ha validado respecto a los problemas (en 2D) de vórtices de Taylor-Green, y el desarrollo de vórticesde Karman en un cilindro cuadrado. La parte acústica resuelve la propagación de ondas descritaspor las ecuaciones linearizadas de Euler, empleando una discretización de Galerkin discontinua. El método se ha validado respecto a la ecuación de Burgers.El método ABS es sencillo de programar con una formulación recursiva. Los resultados demuestran que su sencillez junto con sus altas capacidades de adaptación lo convierten en un método fácilmente extensible a órdenes altos, a la vez que reduce el coste comparado con otros métodos clásicos

A FILTER-FORCING TURBULENCE MODEL FOR LARGE EDDY SIMULATION INCORPORATING THE COMPRESSIBLE POOR MAN\u27S NAVIER--STOKES EQUATIONS

A new approach to large-eddy simulation (LES) based on the use of explicit spatial filtering combined with backscatter forcing is presented. The forcing uses a discrete dynamical system (DDS) called the compressible ``poor man\u27s\u27\u27 Navier--Stokes (CPMNS) equations. This DDS is derived from the governing equations and is shown to exhibit good spectral and dynamical properties for use in a turbulence model. An overview and critique of existing turbulence theory and turbulence models is given. A comprehensive theoretical case is presented arguing that traditional LES equations contain unresolved scales in terms generally thought to be resolved, and that this can only be solved with explicit filtering. The CPMNS equations are then incorporated into a simple forcing in the OVERFLOW compressible flow code, and tests are done on homogeneous, isotropic, decaying turbulence, a Mach 3 compression ramp, and a Mach 0.8 open cavity. The numerical results validate the general filter-forcing approach, although they also reveal inadequacies in OVERFLOW and that the current approach is likely too simple to be universally applicable. Two new proposals for constructing better forcing models are presented at the end of the work

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

High-performance and hardware-aware computing: proceedings of the first International Workshop on New Frontiers in High-performance and Hardware-aware Computing (HipHaC\u2708)

The HipHaC workshop aims at combining new aspects of parallel, heterogeneous, and reconfigurable microprocessor technologies with concepts of high-performance computing and, particularly, numerical solution methods. Compute- and memory-intensive applications can only benefit from the full hardware potential if all features on all levels are taken into account in a holistic approach

Mathematical analysis for tumor growth model of ordinary differential equations

Special functions occur quite frequently in mathematical analysis and lend itself rather frequently in physical and engineering applications. Among the special functions, gamma function seemed to be widely used. The purpose of this thesis is to analyse the various properties of gamma function and use these properties and its definition to derive and tackle some integration problem which occur quite frequently in applications. It should be noted that if elementary techniques such as substitution and integration by parts were used to tackle most of the integration problems, then we will end up with frustration. Due to this, importance of gamma function cannot be denied

An implementation of a numerical advection equation solver on modern graphics cards using compute unified device architecture

Thesis (M.S.) University of Alaska Fairbanks, 2010"In the past decade, the Graphics Processing Unit (GPU) is reported to have become a powerful general-purpose computation platform for various application areas. The Arctic Region Supercomputing Center (ARSC) intends to assess the capability of this emerging computing tool so that they may enlist it as component of supercomputing systems, but at a lower cost. This thesis reports on parallelization, on both GPU and CPU, of a numerical algorithm named the Total Variation Diminishing (TVD) scheme, which is used in the Eulerian Polar Parallel Ionospheric Model (EPPIM) developed at UAF's Geophysical Institute (GI) and ARSC. The GPU (single NVIDIA Tesla® C2050) and CPU (dual Intel Xeon x5560) implementations were parallelized using the Compute Unified Device Architecture (CUDA) language and OpenMP with the C language respectively. A speedup of up to 175x was observed when comparing the CUDA/GPU implementation to the non-parallelized CPU version, and of almost 40x when comparing to the parallelized CPU version. Results also demonstrated an average floating-point-operation rate of 107 GFLOPs, 351 times more than that the CPU version can offer. However, there is still space for improvement as only one tenth of the peak theoretical performance of the C2050 was achieved"--Leaf iii.1. Introduction -- 1.1. Motivation -- 1.2. Similar work -- 1.3. Contribution -- 1.4. Thesis outline -- 2. Background -- 2.1. Evolution of GPU computing -- 2.2. Compute Unified Device Architecture -- 2.2.1. Hardware architecture -- 2.2.2. Software architecture -- 2.2.3. Terminology -- 2.2.4. Compilation workflow -- 2.2.5. CUDA memory model -- 2.2.6. Programming methodology -- 2.2.7. Performance considerations for scientific computing -- 2.3. Mathematical background -- 2.3.1. Continuity equation -- 2.3.2. Numerical schemes -- 2.3.3. The corner transport upwind scheme -- 2.3.4. The Lax-Wendroff scheme -- 2.3.5. The TVD scheme -- 3. Algorithms -- 3.1. Introduction -- 3.2. The serial algorithm -- 3.3. The parallel algorithms -- 4. Performance test and analysis -- 4.1. Hardware configuration -- 4.2. Methodology -- 4.2.1. Testing approach -- 4.2.2. Testing environment -- 4.2.3. Validation -- 4.3. Results and analysis -- 4.3.1. Serial implementation -- 4.3.2. The single-kernal parallel implementation -- 4.3.3. The multi-kernal parallel implementation -- 5. Conclusions and future work -- 5.1. Conclusions -- 5.2. Future work -- References -- Appendix

Aerofoil broadband and tonal noise modelling using Fast-Random-Particle-Mesh method and Large Eddy Simulation

PhD thesisThe aim of this work is to critically examine state-of-the art numerical methods used in computational aero-acoustics with the goal to further develop methods of choice that satisfy the industry requirements for aero-acoustic design, that is being fast, physical and potentially applicable to a variety of airframe noise problems. At the core of this thesis, two different modelling techniques are applied to benchmark aerofoil noise problems. One is based on a modern Fast Random Particle Mesh (FRPM) method with the mean flow and turbulence statistics supplied from the Reynolds-Averaged Navier-Stokes (RANS) simulation. The second technique is a Large Eddy Simulation (LES) method utilising the new in-house fast-turn-around GPU CABARET code. The novelty of the work presented herein consists in the development of new modifications to the stochastic FRPM method featuring both tonal and broadband noise sources. The technique relies on the combination of incorporated vortex-shedding resolved flow available from Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulation with the fine-scale turbulence FRPM solution generated via stochastic velocity fluctuations in the context of vortex sound theory. In contrast to the existing literature, proposed methodology encompasses a unified treatment for broadband and tonal acoustic noise sources at the source level, thus, accounting for linear source interference as well as possible non-linear source interaction effects. Results of the method’s application for two aerofoil benchmark cases, with sharp and blunt trailing edges are presented. In each case, the importance of individual linear and non-linear noise sources was investigated. Several new key features related to the unsteady implementation of the method were tested and brought into the equation. The source terms responsible for noise generation in accordance with the vortex sound theory are computed to assess the validity range of a digital filter calibration parameter used in the FRPM method for synthetic turbulence generation as compared to the same source reconstructed from the first principle LES solution. Such comparison at the source level has been achieved for the first time in the modelling literature, which allows for the physical interpretation of results obtained by the FRPM method. Finally, solutions of the FRPM method with the calibration parameter tailored in accordance with the LES are used for far-field noise predictions which are compared with experimental measurementsBAE Systems Ltd.Engineering and Physical Sciences Research Council (EPSRC)

Flux Reconstruction as a Direct Method for Near-Field Computational Aeroacoustics

The noise produced from commercial aviation is detrimental and strictly regulated at an international level. To satisfy stringent forthcoming noise reduction requirements, current industry standard, lower order aeroacoustic methods used to approximate acoustic fields must be replaced with high-order methods that can more accurately compute the acoustic field, providing invaluable insight into noise generation and potential design optimization processes. In this thesis, the accuracy and performance of high-order numerical methods, as applied in the scope of computational aeroacoustics, are evaluated. Specifically, the high-order flux reconstruction method’s ability to directly compute acoustic fields is assessed. The field of computational aeroacoustics is intrinsically dissimilar to the field of computational fluid dynamics and thus contains highly distinctive numerical challenges. Several verification studies are performed, for a range of polynomial orders, each addressing an individual numerical challenge. It is shown that the high order flux reconstruction method sufficiently resolves each of these numerical challenges, with higher order polynomials providing more accurate and efficient results on a per degree of freedom basis. The high order flux reconstruction method’s proficiency for direct computation of near-field acoustics is validated by performing simulations of flow over a cylinder and a deep cavity and comparing the results against experimental data. Finally, the performance of the high-order flux reconstruction method in industrial applications is assessed by directly computing the acoustic field produced by a NACA0012 airfoil at varying angles of attack

Impact of the unsteady aerothermal environment on the turbine blades temperature

Ce travail de thèse, menée dans le cadre d'une convention CIFRE entre TURBOMECA et le CERFACS, s'inscrit dans un contexte d'amélioration des performances des turbines de type axial équipant les turboréacteurs d'hélicoptère. L'une des principales difficultés rencontrée dans cette démarche concerne la maîtrise de la température que voient les pales de ce composant, notamment la roue haute pression. Les travaux de cette thèse s'articulent autour de deux axes principaux: - Le premier traite l'analyse de la Simulations aux Grandes Echelles (SGE) autour de pales. Une approche numérique SGE sur des maillages non-structurés est comparée aux résultats Reynolds Averaged Navier-Stokes (RANS) sur des maillages structurés, usuels dans ce type de configuration, ainsi qu'à une approche SGE sur maillages structurés. La SGE sur maillage non-structuré démontre sa capacité à prendre en compte les phénomènes qui ont un impact sur les flux de chaleur pariétaux. - Le second axe de recherche a pour objectif de développer un outil numérique de couplage pour assurer le transfert d'information entre un code SGE réactif sur maillage non-structuré, employé dans les chambres de combustion, et un code non-réactif en RANS, utilisé par les industriels pour modéliser l'étage turbine. Cet outil a été validé sur plusieurs cas tests qui montrent le potentiel de cette méthodologie pour le couplage multi-composant. ABSTRACT : This PhD dissertation, conducted as part of a CIFRE research project between TURBOMECA and CERFACS, deals with improving performance of axial turbines from helicopter engines. One of the main difficulties with such an objective is the control of the temperature prediction around the blades, especially the temperature of the high pressure rotor. The work of this thesis focusses on two axes: - First concerns the analysis of Large Eddy Simulation (LES) predictions around blades: a numerical LES approach on unstructured meshes is compared to Reynolds Averaged Navier-Stokes (RANS) results on structured meshes as well as to LES on structured meshes. LES on unstructured meshes demonstrates its capacity of taking into account the phenomena which have an impact on wall heat flux around blades. - The second axis deals with the development of a numerical tool for coupling and transferring information between a reactive LES code, used in combustion chambers, and a non-reactive RANS solver, employed by industrial actors for modeling the turbine stage. This tool is validated on a number of test cases which show the potential of this methodology for multi-component predictions