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Spectral (Finite) Volume Method for One Dimensional Euler Equations

Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.

Wang, Z. J.↗

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

Loh, Ching Y.↗

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗

Temporal Variation of Aerosol Properties at a Rural Continental Site and Study of Aerosol Evolution through Growth Law Analysis

Aerosol size distributions were measured by a Scanning Mobility Particle Sizer (SMPS) onboard the CIRPAS Twin Otter aircraft during 16 flights at the Southern Great Plains (SGP) site in northern central Oklahoma as part of the Aerosol Intensive Operation period in May, 2003. During the same period a second SMPS was deployed at a surface station and provided continuous measurements. Combined with trace gas measurements at the SGP site and back-trajectory analysis, the aerosol size distributions provided insights into the sources of aerosols observed at the SGP site. High particle concentrations, observed mostly during daytime, were well correlated with the sulfur dioxide (SO2) mixing ratios, suggesting nucleation involving sulfuric acid is likely the main source of newly formed particles at the SGP. Aerosols within plumes originating from wildfires in Central America were measured at the surface site. Vertically compact aerosol layers, which can be traced back to forest fires in East Asia, were intercepted at altitudes over 3000 meters. Analyses of size dependent particle growth rates for four periods during which high cloud coverage was observed indicate growth dominated by volume controlled reactions. Sulfate accounts for 50% to 72% of the increase in aerosol volume concentration; the rest of the volume concentration increase was likely due to secondary organic species. The growth law analyses and meteorological conditions indicate that the sulfate was produced mainly through aqueous oxidation of SO2 in clouds droplets and hydrated aerosol particles.

Wang, Jian↗

Development of the Joint NASA/NCAR General Circulation Model

The Data Assimilation Office at NASA/Goddard Space Flight Center is collaborating with NCAR/CGD in an ambitious proposal for the development of a unified climate, numerical weather prediction, and chemistry transport model which is suitable for global data assimilation of the physical and chemical state of the Earth's atmosphere. A prototype model based on the NCAR CCM3 physics and the NASA finite-volume dynamical core has been built. A unique feature of the NASA finite-volume dynamical core is its advanced tracer transport algorithm on the floating Lagrangian control-volume coordinate. The model currently has a highly idealized ozone production/loss chemistry derived from the observed 2D (latitude-height) climatology of the recent decades. Nevertheless, the simulated horizontal wave structure of the total ozone is in good qualitative agreement with the observed (TOMS). Long term climate simulations and NWP experiments have been carried out. Current up to date status and futur! e plan will be discussed in the conference.

Lin, S.-J.↗

Digital Multicasting of Multiple Audio Streams

The Mission Control Center Voice Over Internet Protocol (MCC VOIP) system (see figure) comprises hardware and software that effect simultaneous, nearly real-time transmission of as many as 14 different audio streams to authorized listeners via the MCC intranet and/or the Internet. The original version of the MCC VOIP system was conceived to enable flight-support personnel located in offices outside a spacecraft mission control center to monitor audio loops within the mission control center. Different versions of the MCC VOIP system could be used for a variety of public and commercial purposes - for example, to enable members of the general public to monitor one or more NASA audio streams through their home computers, to enable air-traffic supervisors to monitor communication between airline pilots and air-traffic controllers in training, and to monitor conferences among brokers in a stock exchange. At the transmitting end, the audio-distribution process begins with feeding the audio signals to analog-to-digital converters. The resulting digital streams are sent through the MCC intranet, using a user datagram protocol (UDP), to a server that converts them to encrypted data packets. The encrypted data packets are then routed to the personal computers of authorized users by use of multicasting techniques. The total data-processing load on the portion of the system upstream of and including the encryption server is the total load imposed by all of the audio streams being encoded, regardless of the number of the listeners or the number of streams being monitored concurrently by the listeners. The personal computer of a user authorized to listen is equipped with special- purpose MCC audio-player software. When the user launches the program, the user is prompted to provide identification and a password. In one of two access- control provisions, the program is hard-coded to validate the user s identity and password against a list maintained on a domain-controller computer at the MCC. In the other access-control provision, the program verifies that the user is authorized to have access to the audio streams. Once both access-control checks are completed, the audio software presents a graphical display that includes audiostream-selection buttons and volume-control sliders. The user can select all or any subset of the available audio streams and can adjust the volume of each stream independently of that of the other streams. The audio-player program spawns a "read" process for the selected stream(s). The spawned process sends, to the router(s), a "multicast-join" request for the selected streams. The router(s) responds to the request by sending the encrypted multicast packets to the spawned process. The spawned process receives the encrypted multicast packets and sends a decryption packet to audio-driver software. As the volume or muting features are changed by the user, interrupts are sent to the spawned process to change the corresponding attributes sent to the audio-driver software. The total latency of this system - that is, the total time from the origination of the audio signals to generation of sound at a listener s computer - lies between four and six seconds.

Macha, Mitchell↗

Evaluation of Rotordynamic Coefficients of Look-through Labyrinths by Means of a Three Volume Bulk Flow Model

To describe the compressible, turbulent flow in a labyrinth seal, a three volume bulk flow model is presented. The conservation equations for mass, momentum, and energy are established in every control volume. A perturbation analysis is performed, yielding zeroth order equations for centric rotor position and first order equations describing the flow field for small rotor motions around the seal center. The equations are integrated numerically. From perturbation pressure, the forces on the shaft and the dynamic coefficients are calculated.

Nordmann, R.↗

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

High-Efficiency High-Resolution Global Model Developments at the NASA Goddard Data Assimilation Office

The Data Assimilation Office (DAO) has been developing a new generation of ultra-high resolution General Circulation Model (GCM) that is suitable for 4-D data assimilation, numerical weather predictions, and climate simulations. These three applications have conflicting requirements. For 4-D data assimilation and weather predictions, it is highly desirable to run the model at the highest possible spatial resolution (e.g., 55 km or finer) so as to be able to resolve and predict socially and economically important weather phenomena such as tropical cyclones, hurricanes, and severe winter storms. For climate change applications, the model simulations need to be carried out for decades, if not centuries. To reduce uncertainty in climate change assessments, the next generation model would also need to be run at a fine enough spatial resolution that can at least marginally simulate the effects of intense tropical cyclones. Scientific problems (e.g., parameterization of subgrid scale moist processes) aside, all three areas of application require the model's computational performance to be dramatically improved as compared to the previous generation. In this talk, I will present the current and future developments of the "finite-volume dynamical core" at the Data Assimilation Office. This dynamical core applies modem monotonicity preserving algorithms and is genuinely conservative by construction, not by an ad hoc fixer. The "discretization" of the conservation laws is purely local, which is clearly advantageous for resolving sharp gradient flow features. In addition, the local nature of the finite-volume discretization also has a significant advantage on distributed memory parallel computers. Together with a unique vertically Lagrangian control volume discretization that essentially reduces the dimension of the computational problem from three to two, the finite-volume dynamical core is very efficient, particularly at high resolutions. I will also present the computational design of the dynamical core using a hybrid distributed-shared memory programming paradigm that is portable to virtually any of today's high-end parallel super-computing clusters.

Lin, Shian-Jiann↗

High-Efficiency High-Resolution Global Model Developments at the NASA Goddard Data Assimilation Office

The Data Assimilation Office (DAO) has been developing a new generation of ultra-high resolution General Circulation Model (GCM) that is suitable for 4-D data assimilation, numerical weather predictions, and climate simulations. These three applications have conflicting requirements. For 4-D data assimilation and weather predictions, it is highly desirable to run the model at the highest possible spatial resolution (e.g., 55 kin or finer) so as to be able to resolve and predict socially and economically important weather phenomena such as tropical cyclones, hurricanes, and severe winter storms. For climate change applications, the model simulations need to be carried out for decades, if not centuries. To reduce uncertainty in climate change assessments, the next generation model would also need to be run at a fine enough spatial resolution that can at least marginally simulate the effects of intense tropical cyclones. Scientific problems (e.g., parameterization of subgrid scale moist processes) aside, all three areas of application require the model's computational performance to be dramatically improved as compared to the previous generation. In this talk, I will present the current and future developments of the "finite-volume dynamical core" at the Data Assimilation Office. This dynamical core applies modem monotonicity preserving algorithms and is genuinely conservative by construction, not by an ad hoc fixer. The "discretization" of the conservation laws is purely local, which is clearly advantageous for resolving sharp gradient flow features. In addition, the local nature of the finite-volume discretization also has a significant advantage on distributed memory parallel computers. Together with a unique vertically Lagrangian control volume discretization that essentially reduces the dimension of the computational problem from three to two, the finite-volume dynamical core is very efficient, particularly at high resolutions. I will also present the computational design of the dynamical core using a hybrid distributed- shared memory programming paradigm that is portable to virtually any of today's high-end parallel super-computing clusters.

Lin, Shian-Jiann↗

A Finite Volume Procedure for Thermo-Fluid System Analysis in a Flow Network

This paper describes a finite volume procedure for network flow analysis in a thermofluid system. A flow network is defined as a group of inter-connected control volumes called “nodes” that are connected by “branches”. The mass and energy conservation equations are solved at the nodes and momentum conservation equations are solved at the branches. The flow network also includes solid nodes to account for fluid to solid heat transfer. The heat conduction equation is solved at the solid nodes in conjunction with the flow equations. The properties of a real fluid are calculated using a thermodynamic property program and used in the conservation equations. The system of equations describing the fluid-solid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution method. This procedure has been incorporated into a general-purpose computer program, the Generalized Fluid System Simulation Program, GFSSP. This paper also presents the application and verification of the method by comparison with test data for several applications that include (a) internal flow in a rocket engine turbo-pump, (b) pressurization and loading of a cryogenic propellant tank, (c) fluid transient during sudden opening of valve for priming of an evacuated feed line, and (d) chill down of a cryogenic transfer line with phase change and two phase flows.

Majumdar, Alok↗

Augmented baroreflex heart rate gain after moderate-intensity, dynamic exercise

The occurrence of a sustained vasodilation and hypotension after acute, dynamic exercise suggests that exercise may alter arterial baroreflex mechanisms. Therefore, we assessed systemic hemodynamics, baroreflex regulation of heart rate, and cardiac vagal tone after 60 min of cycling at 60% peak oxygen consumption in 12 healthy, untrained men and women (ages 21-28 yr). We derived sigmoidal carotid-cardiac baroreflex relations by measurement of R-R interval changes induced by ramped, stepwise, R-wave-triggered changes in external neck pressure from 40 to -65 mmHg. We estimated tonic cardiac vagal control with power spectral analysis of R-R interval variability in the respiratory frequency band (0.2-0.3 Hz) during frequency- and tidal volume-controlled breathing. Both mean arterial pressure and total peripheral resistance were reduced postexercise [pressure: from 86 +/- 2 (mean +/- SE) to 81 +/- 2 mmHg; resistance: from 23 +/- 2 to 16 +/- 1 units; both P < 0.05]. Cardiac output was increased postexercise (from 3.9 +/- 0.3 to 5.5 +/- 0.5 l/min, P < 0.05). Both slope and range of the carotid-cardiac baroreflex relation were increased postexercise (slope: from 4.7 +/- 0.7 to 6.1 +/- 0.9 ms/mmHg; range: from 186 +/- 23 to 238 +/- 30 ms, P < 0.05). Respiratory R-R interval variability (cardiac vagal tone) was not changed at any time after exercise, whereas heart rate and plasma norepinephrine levels were elevated. Thus moderate-intensity, dynamic exercise increases heart rate and cardiac output, reduces peripheral vascular resistance, and augments baroreflex responsiveness. Our data suggest that augmented baroreflex heart rate gain restrains rather than contributes to postexercise hypotension, which appears to be mediated predominately by vasodilation.

NASA Discipline Cardiopulmonary↗

Air conditioning system and component therefore distributing air flow from opposite directions

The air conditioning system comprises a plurality of separate air conditioning units coupled to a common supply duct such that air may be introduced into the supply duct in two opposite flow directions. A plurality of outlets such as registers or auxiliary or branch ducts communicate with the supply duct and valve means are disposed in the supply duct at at least some of the outlets for automatically channelling a controllable amount of air from the supply duct to the associated outlet regardless of the direction of air flow within the supply duct. The valve means comprises an automatic air volume control apparatus for distribution within the air supply duct into which air may be introduced from two opposite directions. The apparatus incorporates a freely swinging movable vane in the supply duct to automatically channel into the associated outlet only the deflected air flow which has the higher relative pressure.

Obler, H. D.↗

A model for prediction of STOVL ejector dynamics

A semi-empirical control-volume approach to ejector modeling for transient performance prediction is presented. This new approach is motivated by the need for a predictive real-time ejector sub-system simulation for Short Take-Off Verticle Landing (STOVL) integrated flight and propulsion controls design applications. Emphasis is placed on discussion of the approximate characterization of the mixing process central to thrust augmenting ejector operation. The proposed ejector model suggests transient flow predictions are possible with a model based on steady-flow data. A practical test case is presented to illustrate model calibration.

Drummond, Colin K.↗

Low-Pressure Generator Makes Cleanrooms Cleaner

Scientists at NASA's Kennedy Space Center work in cleanrooms: laboratories with high degrees of cleanliness provided by strict control of particles such as dust, lint, or human skin. They are contaminant-free facilities, where the air is repeatedly filtered, and surfaces are smooth to prevent particles from getting lodged. Technicians working in these environments wear specially designed cleanroom "bunny suits" and booties over their street clothes, as well as gloves and face masks to avoid any contamination that may be imparted from the outside world. Even normal paper is not allowed in cleanrooms, only cleanroom low-particulate paper. These are sensitive environments where precision work, like the production of silicon chips or hard disk drives, is performed. Often in cleanrooms, positive air pressure is used to force particles outside of the isolated area. The air pressure in the Kennedy cleanrooms is monitored using high-accuracy, low-differential pressure transducers that require periodic calibration. Calibration of the transducers is a tricky business. In prior years, the analysis was performed by sending the transducers to the Kennedy Standards Laboratory, where a very expensive cross-floated, labor- intensive, dead-weight test was conducted. In the early 1990s, scientists at Kennedy determined to develop a technique and find equipment to perform qualification testing on new low-differential pressure transducers in an accurate, cost-effective manner onsite, without requiring an environmentally controlled room. They decided to use the highly accurate, cost-effective Setra Model C264 as the test transducer. For qualification testing of the Setra, though, a portable, lower-cost calibrator was needed that could control the differential pressure to a high degree of resolution and transfer the accuracy of the Standards Laboratory testing to the qualification testing. The researchers decided that, to generate the low-differential pressure setpoints needed for qualification testing, very small gas volume changes could be made against the test article, and a corresponding pressure change would be detected by a pressure standard. This allowed the researchers to recreate cleanroom air pressure settings without the use of a cleanroom. Thus was born the low-differential pressure generator. In 1993, a prototype was developed using a pair of PVC tanks, a volume controller, and a 1-pound-per-square-inch pressure standard. By 1995, the prototype was perfected into the unit that is still used today.

Source record↗

Unstructured multigrid through agglomeration

In this work the compressible Euler equations are solved using finite volume techniques on unstructured grids. The spatial discretization employs a central difference approximation augmented by dissipative terms. Temporal discretization is done using a multistage Runge-Kutta scheme. A multigrid technique is used to accelerate convergence to steady state. The coarse grids are derived directly from the given fine grid through agglomeration of the control volumes. This agglomeration is accomplished by using a greedy-type algorithm and is done in such a way that the load, which is proportional to the number of edges, goes down by nearly a factor of 4 when moving from a fine to a coarse grid. The agglomeration algorithm has been implemented and the grids have been tested in a multigrid code. An area-weighted restriction is applied when moving from fine to coarse grids while a trivial injection is used for prolongation. Across a range of geometries and flows, it is shown that the agglomeration multigrid scheme compares very favorably with an unstructured multigrid algorithm that makes use of independent coarse meshes, both in terms of convergence and elapsed times.

Venkatakrishnan, V.↗

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗

Prediction of Film Cooling on Gas Turbine Airfoils

A three-dimensional Navier-Stokes analysis tool has been developed in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine airfoils. An existing code (Arnone et al., 1991) has been modified for the purpose. The code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. Eigenvalue scaled artificial dissipation and variable-coefficient implicit residual smoothing are used with a full-multigrid technique. Moreover, Mayle's transition criterion (Mayle, 1991) is used. The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the airfoil surface. Each hole exit is represented by several control volumes, thus providing an ability to study the effect of hole shape on the film-cooling characteristics. Comparison is fair with near mid-span experimental data for four and nine rows of cooling holes, five on the shower head, and two rows each on the pressure and suction surfaces. The computations, however, show a strong spanwise variation of the heat transfer coefficient on the airfoil surface, specially with shower-head cooling.

Garg, Vijay K.↗