High Performance Computing in Science and Engineering `07: Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2007


Chapters (33)

We give an overview of the problems and the current status of our twodimensional (core collapse) supernova modelling, and discuss the system of equations and the algorithm for its solution that are employed in our code. In particular we report our recent progress, and focus on the ongoing calculations that are performed on the NEC SX-8 at the HLRS Stuttgart. Especially, we will argue that it might be possible that neutrino-driven supernova explosions set in at much later times than previously considered. This, of course, enhances the need of a code that can make efficient use of the multi-node capability of the NEC SX-8 for long-time simulations of the postbounce evolution of collapsing stellar cores.
The main purpose of particle physics is the explanation of the fundamental mechanism for the interaction of the elementary particles. On the experimental side the investigations take mainly place at the big accelerators at CERN (Geneva) or FERMILAB (Chicago). On the other hand it it essential to develop theoretical models which describe the fundamental interactions and which, of course, have to be confronted with the experiment.
In suspensions of colloidal particles different types of interactions are in a subtle interplay. In this report we are interested in sub-micro meter sized Al2O3 particles which are suspended in water. Their interactions can be adjusted by tuning the pH-value and the salt concentration. In this manner different microscopic structures can be obtained. Industrial processes for the production of ceramics can be optimized by taking advantage of specific changes of the microscopic structure. To investigate the influences of the pH-value and the salt concentration on the microscopic structure and the properties of the suspension, we have developed a coupled Stochastic Rotation Dynamics (SRD) and Molecular Dynamics (MD) simulation code. The code has been parallelized using MPI. We utilize the pair correlation function and the structure factor to analyze the structure of the suspension. The results are summarized in a stability diagram. For selected conditions we study the process of cluster formation in large scale simulations of dilute suspensions.
Transport properties of strongly interacting quantum systems are a major challenge in todays condensed matter theory. While much is known for transport properties of non-interacting electrons, based on the Landauer Büttiker formalism, the non equilibrium properties of interacting fermions are an open problem. Due to the vast improvements in experimental techniques there is an increasing theoretical interest in one-dimensional quantum systems. Since in low dimension the screening of electrons is reduced the effective interaction gets increased and can drive the electron systems into new phases beyond the standard description of a Fermi liquid, e.g. into a Luttinger liquid.
We present electronic band structures for the (110), and (100) PbTe/ CdTe interfaces. The first principles calculations are based on large supercells containing a large number of atoms, which have to be treated fully quantum mechanically. The treatment of free standing nanodots is conceptual more difficult. For the nearly ionic IV-VI semiconductor nanodots we introduce a novel passivation scheme to model the dot-vacuum interfaces. First results for the electronic structure of PbTe nanodots embedded in a CdTe matrix are presented.
A new interface structure, the cross double tetrahedron Si-4N-4Ti, is reported in this paper. To find out the atomic structure of Ti-Si-N superhard nanocomposite coatings, total energy calculations for the different configurations of TiN with Si addition were performed with the ab initio method. The calculation results indicate that (a) there is no interstitial solid solution of Si in the TiN crystallite under the equilibrium condition; (b) the basic structure of the Ti-Si-N composite is the TiN crystallite with the cross double tetrahedron Si-4N-4Ti in the boundary of TiN. The cross double tetrahedron Si-4N-4Ti is an intrinsic mismatch to the B1-NaCl structure of TiN and it fills the boundary with the covalent combination. The TiN boundary is strengthened and the inter diffusion through the boundary is restricted by the interface Si-4N-4Ti so that the hardness and the thermal stability of Ti-Si-N coatings are enhanced. As a fixation element to the rock salt structure, the potential value of the cross double tetrahedron is in the mass production of nanometer patterns or the quantum dots. The formation of the Si-4N-4Ti in the film growth process is also studied. The study indicates that Si-4N-4Ti cannot be formed in the island of TiN on the TiN(001) surface. Under some process conditions, Si will stay outside the island of TiN. The investigation of the Si distribution in TiN demonstrates that the congregation of the Si-4N-4Ti structures in TiN will result in an increase in the local strain and a decrease in the cohesive energy of the system.
For the understanding of physical processes on a molecular scale it is convenient to study the underlying dynamics by wavepacket propagation. Many different propagation schemes have been developed in the past, reaching from the numerically exact standard method, that can only treat very small systems to approximate ones like the time dependent Hartree method (TDH). One of those methods, the multi-configuration time-dependent Hartree (MCTDH) method, has been developed in Heidelberg and it has proved its capability to treat large systems (> 9 degrees of freedom) fully quantum mechanically and with high accuracy.
Ionic liquids (IL) or room temperature molten salts are alternatives to “more toxic” liquids [1]. Their solvent properties can be adjusted to the particular problem by combining the right cation with the right anion, which makes them designer liquids. Usually an ionic liquid is formed by an organic cation combined with an inorganic anion [2, 3]. Further discussions on the subject can be found in the following review articles [4–6].
Oxidation phenomena on the surface of cobalt-based alloys are of large technological relevance and deep scientific importance, since the skin of “native oxide” which covers the surface governs the chemical and physical interactions of the metal with the outer environment. In particular in the case of alloys used in biomedical implantations, such as for instance CoCrMo, the structure and composition of the native oxide layers directly influence the behaviour of implants within the chemically aggressive physiological environment. Understanding and predicting this behaviour requires a precise knowledge of the structure and composition of the ultrathin oxide layer which form spontaneously when a bare alloy surface is put in contact with an oxidising environment.
A multivariate assumed PDF approach together with finite-rate chemistry is used for the simulation of scramjet combustors. Because the combustor entrance conditions of scramjets at low flight Mach numbers (Ma ≈ 8) are close to the ignition limit of hydrogen air mixtures, detailed kinetic schemes are required and an accurate simulation of temperature and temperature fluctuations is essential. In the present paper, a lobed strut injector concept is used for hydrogen injection which enhances the mixing process by production of streamwise vorticity. The influence of the chosen combustor geometry on the mixing behaviour is investigated in this paper. Moreover a Mach 2 supersonic combustion experiment is simulated to investigate the influence of the chosen reaction mechanism and of the assumed PDF model. A detached flame is obtained and the predicted ignition length is a measure for the accuracy of the used kinetic scheme and the modeling of turbulence chemistry interaction.
The mathematical modeling of swirling flames is a difficult task due to the intense coupling between turbulent transport processes and chemical kinetics in particular for instationary processes like the combustion induced vortex breakdown. In this paper a mathematical model to describe the turbulence-chemistry interaction is presented. The described method consists of two parts. Chemical kinetics are taken into account with reduced chemical reaction mechanisms, which have been developed using the ILDM-Method (“Intrinsic Low-Dimensional Manifold”). The turbulencechemistry interaction is described by solving the joint probability density function (PDF) of velocity and scalars. Simulations of test cases with simple geometries verify the developed model.
Numerical simulations of the ignition process of methanol and nheptane droplets in a laminar convective environment are performed using detailed reaction mechanisms and detailed transport models. The ignition delay time of a single droplet is found to decrease with increasing velocity of the convective gas flow. This decrease is attributed to the steepening of the spatial gradients of the profiles of physical variables, like species mass fractions or temperature. This steepening is originated by a stronger gas flow and leads to a speed-up of the physical transport processes. A downstream movement of the local ignition point with increasing flow velocity is observed. For higher flow velocities an ignition in the wake of the droplet followed by an upstream flame propagation is found. After ignition an envelope flame is formed. The structure of this envelope flame is studied.
Direct numerical simulations of a short laminar separation bubble and its bursting are carried out. The bubble is developing on a flat plate due to an externally imposed pressure gradient. Laminar-turbulent transition is triggered by small disturbance input with fixed frequency to keep the bubble short. The short bubble reaches a statistically steady state, while switching off disturbance input yields a growing separation bubble. This phenomenon is denoted as bubble-bursting process. Disturbance input does not only prevent bursting, but can also serve to control the short bubble. Bubble size decreases with increased disturbance amplitude. Performance data on a NEC SX-8 super computer are compared for two different resolutions.
The numerical simulation of liquid jets emerging from hole-type nozzles has received considerable attention since sophisticated numerical schemes and growing computational power have become available. The reason for the efficiency of this novel approach is associated with high numerical accuracy and the simplified numerical setup compared to experiments. Due to this fact, several numerical experiments can be conducted by varying the influencing parameters in order to identify the most influencing factors. The high numerical accuracy of a direct numerical simulation (DNS) is basically achieved by capturing all appearing lengthscales in the flow which are in the order of the usually extremely fine spatial discretization and therefore turbulence modeling is not required. Since preliminary results have shown that the influence of the mean velocity profile can also have a strong influence on the disintegration of the jet, this paper mainly focuses on the influence of the mean axial velocity profile resulting from the variation of the nozzle design. It was found that the kinetic energy per unit mass is one of the major influencing parameters. Additionally bubbly inflows consisting of liquid and air have been regarded in this context. With respect to the numerical accuracy of the presented results, three different grid resolutions were tested in order to identify the influence of the spatial discretization.
Direct Numerical Simulations (DNS) of heat transfer from a flat plate affected by free-stream fluctuations are performed at three different Reynolds numbers. A contoured upper wall is employed to generate a favourable pressure gradient along a large portion of the flat plate. The free-stream fluctuations stem from a separate LES of isotropic turbulence in a box. In the laminar portions of the accelerating boundary layer flow, the formation of streaks was observed to induce an increase in heat transfer by exchange of hot fluid near the surface of the plate and cold fluid from the free-stream. Compared to the accompanying fully laminar simulations (without free-stream fluctuations), in the simulations with free-stream fluctuations the increase in heat transfer in the fully turbulent part of the boundary layer was found to be significantly larger than the increase in heat transfer induced by the formation of streaks in the laminar part. The computations were carried out on the HP-XC1 cluster in Karlsruhe using up to 64 processors and 137 million grid points.
The objective of the project DIMPLE is to study complex turbulent flows over a dimpled surface which is expected to lead to drag reduction compared to a smooth surface. In order to understand the physical mechanism of the flow over an arrangement of shallow dimples, CPU time-consuming direct numerical simulations were carried out using two different grid resolutions and three different configurations. As a first step within this project, the code LESOCC was evaluated and optimized for the new vector machine NEC SX-8. Classical vector systems still combine excellent performance with a well-established optimization approach. On the other hand, clusters based on commodity microprocessors offer comparable peak performance at much lower costs. In the context of the introduction of the NEC SX-8 vector computer series we compare single and parallel performance of a computational fluid dynamics application on the SX-8 and on the SGI Altix architecture demonstrating the potential of the SX-8 for teraflop computing in the area of turbulence research and flow control. Finally, results of the flow predictions over a dimpled surface are presented and compared with the reference case of plane channel flow with smooth walls.
Sound generation of a subsonic laminar jet has been investigated using direct numerical simulation (DNS). The simulation includesthe nozzle end, modelled by a finite flat splitter plate with Mach numbers of MaI = 0.8 above and MaII = 0.2 below the plate. Behind the nozzle end, a combination of wake and mixing layer develops. Due to its instability, roll up and pairing of spanwise vortices occur, with the vortex pairing being the major acoustic source. As a first approach for noise reduction, a rectangular notch at the trailing edge is investigated. It generates longitudinal vortices and a spanwise deformation of the flow Downstream of the nozzle end. This leads to a an early breakdown of the large spanwise vortices and accumulations of small-scale structures. Compared to a two-dimensional simulation performed earlier [3], the emitted sound is reduced by 6 dB.
Results from two Direct Numerical Simulations of a round jet in crossflow with velocity ratio of 3.3 are presented. The Reynolds number was 650 and 325. A passive scalar with Schmidt number of unity is introduced with the jet. The boundary conditions for both, jet and crossflow are laminar. This provides an unambiguous definition of the setup and favours its use as a test case. Transition of the jet was identified by an abrupt expansion of the average scalar field. The higher Reynolds number leads to a transition at 3.49 diameters downstream of the jet exit, the lower one – at 4.41 diameters. The higher Reynolds number flow exhibits smaller turbulent structures, but despite this and the different location of the transition, the trajectories of the two flows are close to each other. The computational technique employed is a block-structured Finite-Volume method with local grid refinement at block boundaries implemented in the code LESOCC2. This allowed efficient distribution of cells so that 89% of them could be clustered in the vicinity of the jet exit and in the transition region. Issues of parallelization and efficiency are addressed in the text.
We numerically simulate turbulent flow in a horizontal plane channel over a bed of mobile spherical particles. All scales of fluid motion are resolved without modeling and the phase interface is accurately represented. Direct contact between particles is taken into account by an artificial short-range repulsion force. Our results indicate possible scenarios for the onset of erosion through collective motion induced by buffer-layer streaks and subsequent saltation of individual particles.
The flow field and the acoustic field of various jet flows and a high-lift configuration consisting of a deployed slat and a main wing are numerically analyzed. The flow data, which are computed via large-eddy simulations (LES), provide the distributions being plugged in the source terms of the acoustic perturbation equations (APE) to compute the acoustic near field. The investigation emphasizes the core flow to have a major impact on the radiated jet noise. In particular the effect of heating the inner stream generates substantial noise to the sideline of the jet, whereas the Lamb vector is the dominant noise source for the downstream noise. Furthermore, the analysis of the airframe noise shows the interaction of the shear layer of the slat trailing edge and the slat gap flow to generate higher vorticity than the main airfoil trailing edge shear layer. Thus, the slat gap is the more dominant noise region for an airport approaching aircraft.
A highly-resolved Large Eddy Simulation of high Reynolds number flow over and around a three-dimensional hill is currently being performed on the NEC SX-8. The principal aim of the study is to generate target results against which Hybrid LES-RANS methods can be validated. The complex flow separation in the lee of the hill is illustrated by displaying streamlines of the mean flow at different heights. The instantaneous structures which appear in the wake of the hill are also discussed.
The flow inside a simplified one-stroke engine with squared cross section has been calculated with compressible Large Eddy Simulation (LES) using our code SPARC and compared with the measurements on the same geometry. The one-stroke engine has a turbulence generator, which can ether generate a tumble or homogenous turbulence depending on the configuration. By waiting different amount of time after the turbulence generation process a variable turbulence level can be achieved. During the up going motion of the piston the turbulent fuel mixture is compressed and ignited by a row of spark plugs. The simulation has been using more then 8 million points for the space discretization. A space conservation law was used to calculate the grid motion with Euler-Lagrange technique. The mesh was refined in the shear layers and close to the wall so that y+ < 1 results almost everywhere. A comparison between Miles (monotonically integrated large eddy simulation) approach and conventional subgrid scale modelling (dynamic Smagorinsky) showed very similar solutions. Mean and fluctuating velocities at TDC are compared with available experimental findings.
In this paper the three-dimensional non-reacting turbulent flow field of a swirl-stabilized gas turbine model combustor is analysed with compressible CFD. For the flow analysis URANS and Hybrid RANS/LES (DES, SAS) turbulence models were applied. The governing equations and the numerical method are described. The simulations were performed using the commercial CFD software package ANSYS CFX-10.0. The numerically achieved velocity components show a good agreement with the experimental values obtained by Particle Image Velocimetry (PIV). Furthermore, a precessing vortex core (PVC) could be found in the combustion chamber. The simulations were performed on the HP XC4000 system of the High Performance Computing Centre Karlsruhe.
The hybrid particle-level-set method (HPLS) is an extension of the established level-set technique and allows for an efficient description of moving interfaces. With level-set methods phase interfaces are treated implicitly and hence complex shape changes as well as merging and breaking up of geometries can be handled. The HPLS-method additionally employs marker particles to improve massconservation properties of the classical level-set scheme. Subject of the present paper is the efficient implementation and the application to large-scale computations of this method. In simulations of two-phase flows the major part of computational operations for the multi-phase model occur in the vicinity of the interface. The implementation of these operations on parallel vector systems requires special attention. Computational results of gas bubbles rising in liquids show good agreement with the experimental data and confirm the efficiency and accuracy of the HPLS-scheme.
Large scale lattice Boltzmann simulations are utilized to investigate spinodal decomposition and structuring effects in binary immiscible and ternary amphiphilic fluid mixtures under shear. We use a highly scalable parallel Fortran 90 code for the implementation of the simulation method and demonstrate that adding surfactant to a system of immiscible fluid constituents can change the mixture’s properties profoundly: stable bicontinuous microemulsions form which undergo a transition from a sponge to a lamellar phase by applying a constant shear. Under oscillatory shear tubular structures can be observed.
A numerical and experimental analysis of scramjet intake flows has been initiated at RWTH Aachen University as part of the Research Training Group GRK 1095: “Aero-Thermodynamic Design of a Scramjet Engine for a Future Space Transportation System”. This report presents an overview of the ongoing work on the numerical simulations of air intake flow using two different, well validated Reynolds averaged Navier Stokes solvers. Several geometry concepts e.g. 2D intake, 3D intake using a single or double ramp configuration were investigated. One example for the so-called 2D intake can be seen in Fig. 1 and for a 3D intake in Fig. 2. To analyze the effects these different geometries have on the flow, especially on the separation bubble in the isolator inlet as well as on transition and efficiency, several numerical simulations (2D and 3D) were performed using a variety of turbulence models. Mostly the Spalart–Allmaras – one equation model and the so called SSG–Reynolds stress model by Speziale, Sakar and Gatski were used. The data obtained will be compared with experimental results. These experiments started in March 2007. It has to be said that not all results presented here were achieved using the NEC computing cluster. For comparison several calculations were conducted on the IBM Jump system of the Jülich Research Centre and on the SUN cluster of RWTH Aachen University. At the end of this report we give comments on the computational performance.
In this paper we present numerical simulation results of a complete helicopter configuration. The CFD code FLOWer (DLR) is used for the simulation of the aerodynamics. For the main rotor an aeroelastic analysis is performed using weak fluid-structure coupling between FLOWer and the flight mechanics code HOST (Eurocopter). As a reference configuration the complete helicopter configuration investigated in the EU project GOAHEAD has been chosen.
Modern processors reach their performance speedup not merely by increasing clock frequency, but to a greater extend by fundamental changes and extensions of the processor architecture itself. These extensions require the application developer to adapt programming techniques to exploit the existing performance potential. Otherwise the situation may arise that the processor becomes nominally faster, but the application doesn’t run faster [3, 4]. A limiting factor for computations is memory access. There is an ever increasing discrepancy between CPU cycle time and main storage access time. Fetching data is expensive in terms of CPU being idle. To narrow the gap between smaller CPU cycle times and possible access times of main storage in general, a rapid access temporary storage between CPU and main storage was introduced, the so-called cache. The basic idea of a cache is to store data following the locality of reference principle. Latency is reduced if a subsequently requested datum is found in the faster cache instead of having to transfer it from slow main storage. Given a sufficient locality of the data, i.e. the data of preceding accesses is still cached, the number of accesses to the cache will exceed those to slow main storage. Throughput can be increased significantly this way. Access to main storage will not be faster with any access sample automatically, but only if the program uses mainly data being already in the cache. This requires appropriate adjustments being made to the applications [2].
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is a Fourier transform mid-infrared limb scanning high resolution spectrometer for measurement of more than 30 atmospheric trace species related to atmospheric chemistry and global change. At the Institute for Meteorology and Climate Research (IMK), measured radiance spectra are used for retrieval of altitude-resolved profiles of abundances of different trace species of the atmosphere (H2O, O3, N2O, CH4, NO2, HNO3, NO, CO, CFC-11, CFC-12, HCFC-22, CFC-113, HCFC-142b, H2O2, HDO, ClONO2, N2O5, HO2NO2, HOCl, ClO, C2H6, SF6, NH3, OCS, HCN, HCOOH, PAN, acetone, CH3CN, and others). These 4-D trace gas distributions are used for the assessment of (a) stratospheric ozone chemistry (b) stratospheric cloud physics and heterogeneous chemistry (c) tropospheric stratospheric exchange (d) intercontinental transport of pollutants in the upper troposphere (e) mesospheric stratospheric exchange (f) effects of solar proton events on stratospheric chemistry. While data analysis strategy developed at IMK over the last fifteen years has proven successful for atmospheric case studies of limited spatial and temporal coverage, numerous research topics require either a complete global data set, or the retrieval of many different species, or both. These requirements cannot be fulfilled by IMK’s limited computational resources. The opportunity to process major parts of the data on the XC supercomputers therefore offers a unique chance to improve not only the quantity of processed data but also the quality, because in the same time more species can be processed, which leads to a more thorough picture of middle atmosphere chemistry. After the successful transfer of the core processing tools to the XC1/XC2 several projects have already been processed partly on these supercomputers. Examples of projects are given and the process of tool transfer and adaptation is discussed as well as the current performance and remaining problems and potential sources for further optimization.
Already a quick glance at regional climatic maps, for instance the ones prepared for the State of Baden-Wuerttemberg [1], shows that near surface temperature, wind and precipitation can vary strongly over distances of about ten kilometres and less. In order to assess the regional impact of climatic change, we therefore need information at such small spatial scales. The only way to obtain information on the future climate is by using global climate models. Their resolution, being in the order of more than 100km even for the most recent models (the presently used ECHAM5 model at the Max-Planck-Institut for Meteorology has a resolution of about 150km in our latitudes), however, is much too coarse for impact studies, lest for detailed planning purposes. At such resolutions, terrain height is smoothed resulting in over-/ underestimation of valley/mountain heights (e.g. in the Black Forest) by several 100 m; this can result in large errors for quantities which are closely related to terrain height, like temperature, precipitation and wind. Furthermore, subgrid-scale features like urban areas, valleys and mountains which can have considerable influence on regional climate are not taken into account. The same is true for subgrid-scale climatically relevant processes, like convective summer precipitation (thunderstorms), which have to be parameterised. This problem is similar to the closure problem in turbulence, perhaps with the difference that the cloud physical processes involved are less known and the parameterisations are even more uncertain.
The focus of this paper is numerical modeling of crust-mantle differentiation. We begin by surveying the observational constraints of this process. The present-time distribution of incompatible elements are described and discussed. The mentioned differentiation causes formation and growth of continents and, as a complement, the generation and increase of the depleted MORB mantle (DMM). Here, we present a solution of this problem by an integrated theory that also includes the thermal solid-state convection in a 3-D compressible spherical-shell mantle heated from within and slightly from below. The conservation of mass, momentum, energy, angular momentum, and of four sums of the number of atoms of the pairs 238U- 206Pb, 235U-207Pb, 232Th-208Pb, 40K-40Ar is guaranteed by the used equations. The pressure- and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, σy . No restrictions are supposed regarding number, size, form and distribution of continents. Only oceanic plateaus touching a continent have to be united with this continent. This mimics the accretion of terranes. The numerical results are an episodic growth of the total mass of the continents and acceptable courses of the curves of the laterally averaged surface heat flow, qob, the Urey number, Ur, and the Rayleigh number, Ra. In spite of more than 4500 Ma of solid-state mantle convection, we typically obtain separate, although not simply connected geochemical mantle reservoirs. None of the reservoirs is free of mixing. This is a big step towards a reconciliation of the stirring problem. As expected, DMM strongly predominates immediately beneath the continents and the oceanic lithosphere. Apart from that, the result is a marble-cake mantle but DMM prevails in the upper half of the mantle. We find Earth-like continent distributions in a central part of Ra-σy plot obtained by a comprehensive variation of parameters. There are also Ra-σy areas with small deviations of the calculated total continental volume from the observed value, with acceptable values of Ur and with realistic surface heat flow. It is remarkable that all of these different acceptable Ra-σy regions share a common overlap area. We compare the observed present-time topography spectrum and the theoretical flow spectrum n 1/2 × (n + 1)1/2 × (v 2n,pol ).
Human-environment thermal interactions play an important role in numerous areas of human endeavour from the safety of fire-fighters, thermal comfort in buildings to energy efficient planning of heating and ventilation systems. The thermal interactions that occur between humans and their immediate environments are however very complex and thus difficult to predict. The project currently being carried out at Building Sciences Group (fbta) at the University of Karlsruhe started in March 2006. This project is part of a four year research project in collaboration with the Institute of Energy and Sustainable Development (IESD) at the De Montfort University in Leicester, UK and the Technical University of Denmark. The focus is on the complex human-environment interactions in naturally ventilated buildings to predict human thermal comfort. To correctly predict the thermo-physiological interactions of humans with their surroundings that dictate the perception of thermal comfort, an advanced and widely validated cybernetic multi-segmental thermophysiological model namely “IESD Fiala Model” is employed. The model is used to provide the necessary physiological data as boundary conditions for Computational Fluid Dynamics (CFD) simulations incorporating a detailed geometry model of the human body and the surrounding space. CFD techniques can predict in detail the spatial variations of air temperature, air speed, turbulence intensity, radiation effects on heat transfer, moisture and pollutant concentrations. At the moment a number of CFD codes exist, but due to time constraints only ANSYS CFX Version 10.0 [1] is used in this project.
Weighted extended B-splines (web-splines) combine the computational efficiency of B-splines and the geometric flexibility of standard finite elements on unstructured meshes. These new finite elements on uniform grids (cf. [5] and www.webspline. de) are ideally suited for vectorization, parallelization and multilevel techniques. In this project we explore the potential of the web-method for large scale applications with performance tests on the NEC SX-8 cluster of the HLRS. We implement a new minimal degree variant which uses predefined instruction sequences for matrix assembly and is almost as efficient as a difference scheme on rectangular domains.
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