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58 records · Page 4

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NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS2000

Free-Flying Magnetometer Data System

The Free-Flying Magnetometer (FFM) is an autonomous "sensorcraft" developed at the Jet Propulsion Laboratory (JPL) for the Enstrophy sounding rocket mission. This mission was a collaborative project between the University of New Hampshire, Cornell University and JPL. The science goal of the mission was the study of current filamentation phenomena in the northern auroral region through multipoint measurements of magnetic field. The technical objective of the mission was the proof of concept of the JPL FFM design and the demonstration of an in-situ multipoint measurement technique employing many free-flying spacecraft. Four FFMs were successfully deployed from a sounding rocket launched from Poker Flats, Alaska on February 11, 1999. These hockey-puck-sized (80 mm diameter, 38 mm. height, 250 gram mass) free flyers each carry a miniature 3-axis flux-gate magnetometer that output +/- 2 V signals corresponding to a +/- 60,000 nT measurement range for each axis. The FFM uses a synchronized four-channel Sigma(Delta) Analog-to-Digital Converter (ADC) having a dynamic range of +/- 2.5V and converting at a rate of 279 samples/second/channel. Three channels are used to digitize the magnetometer signals to 17-bit (1.144 nT/bit) resolution. The fourth ADC channel is multiplexed for system monitoring of four temperature sensors and two battery voltages. The FFM also contains two sun sensors, a laser diode which emits a fan-shaped beam, a miniature S-band transmitter for direct communication to the ground station antennas, an ultra-stable Temperature Compensated Crystal Oscillator (TCXO) clock, an integrated data subsystem implemented in a Field-Programmable Gate Array (FPGA), a 4 Mbit Static Random Access Memory (SRAM) for data storage and Lithium Thionyl Chloride batteries for power. Communicating commands to the FFM prior to deployment is achieved with an infrared (IR) link. The FFM IR receiver responds to 9-bit pulse coded signals that are generated by an IR Light Emitting Diode (LED) in the payload for turning FFM power on or off and placing the FFM in a test mode or flight mode. The IR links are also used to synchronize (zero) the clocks onboard all the FFMs through a reset pulse originating from the payload GPS receiver that is issued when the FFMs are in flight mode. The FPGA based data subsystem manages continuous data collection from the four ADC channels and sun sensors, formatting and storing the data to SRAM, and controlling downlink transmission. The transmitter is powered only after a 2547 frame SRAM buffer has been filled (approx. 5 minutes of data). The data is Viterbi encoded and sent to the S-band transmitter via a First-In-First-Out (FIFO) buffer who's output is clocked at 100 bits/second. After the 26-second transmission, the transmitter is turned off to reduce noise coupling to the sensitive magnetometer. The data subsystem control consists of a master state machine that performs data flow management and is interfaced through a prioritized interrupt scheme to state machines that service the ADC, sun sensors and transmitter FIFO. Continuous data collection prevents the missing of data during transmission and provides implicit time tagging of the data acquired by the ADC because of synchronization with the TCXO clock.

Blaes, B.↗