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NASA NTRS1993

Euler solutions for blunt bodies using triangular meshes - Artificial viscosity forms and numerical boundary conditions

A finite volume method is used to calculate compressible inviscid flows over blunt bodies using, in general, unstructured grids. Artificial viscosity forms are derived based on a simplified least squares procedure. The extra second order terms are consistent with the governing equations, hence a systematic treatment of the numerical boundary conditions can be easily implemented. A special treatment of blunt bodies may be required. The discrete equations are linearized and the resulting system is solved by a relaxation method. Preliminary results indicate that the effect of the numerical dissipation is minimal. For subsonic flows over smooth bodies, the solution is practically vorticity-free and the total pressure loss is of the same order as the truncation error. Finally, some extensions of the present method are briefly discussed.

Winterstein, R.↗

NASA NTRS1993

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗

NASA NTRS1992

Finite-element solution scheme for compressible viscous flow

Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.

Hassan, O.↗

NASA NTRS1993

Adaptive computations of flow around a delta wing with vortex breakdown

An adaptive unstructured mesh solution method for the three-dimensional Euler equations was used to simulate the flow around a sharp edged delta wing. Emphasis was on the breakdown of the leading edge vortex at high angle of attack. Large values of entropy, which indicate vortical regions of the flow, specified the region in which adaptation was performed. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, and demonstrate the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, showing good agreement in cases in which vortex breakdown is located over the wing.

Modiano, David L.↗

NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for hypersonic flowfield simulations on supercomputers

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The relaxation strategy is well suited for computers employing either vector or parallel architectures, and the relation between computer architecture and algorithm is emphasized. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large. block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over a blunt body. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km.) over the Aeroassist Flight Experiment (AFE) configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗

NASA NTRS1993

The response of the high-latitude dayside ionosphere to an abrupt northward transition in the IMF

We examine the response of the high-latitude ionosphere in the prenoon sector to a northward turning of the IMF. The event was observed in the 11-13 UT interval on June 1, 1987, in the course of a multiday SUNDIAL campaign. The transition in the IMF was observed by the IMP-8 satellite which was located upstream of the earth at a distance of 36 Re. The ionospheric response in the 70-80 deg invariant latitude interval was monitored by two radars. The preexisting plasma convection observed by the radars exhibited large velocities (500-1000 m/s) and stable longterm trends, consistent with the inertial rotation of the convection pattern expected of the conditions then prevailing, B(z) less than 0, B(y) greater than 0. The plasma flow rapidly abated in response to the IMF transition. The electron density measurements made by radar in the meridional plane showed that the ionosphere had been rich in structure with the active deposition of ionization by particle precipitation. Subsequently it resembled an inactive, unstructured mid-latitude configuration. There was a dramatic decrease in the amount of backscatter observed by the HF radar. We analyze the times of transition in the various data sets and show that the ionosphere began to show the effects of the IMF transition about 2 min after its probable arrival at the magnetopause boundary.

Ruohoniemi, J. M.↗

NASA NTRS1990

Active flutter and gust response control

After a short recall concerning the aeroelastic equations, active control law based on optimal stochastic control theory is synthesized for a wing flutter and gust response. Robustness of the control system due to structured and unstructured uncertainties is considered. Robustness recovery technique is applied to improve the stability margin.

Oli, Muluneh↗

NASA NTRS1993

Looking for O(N) Navier-Stokes solutions on non-structured meshes

Multigrid methods are good candidates for the resolution of the system arising in numerical fluid dynamics. However, the question is to know if those algorithms which are efficient for the Poisson equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a full multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.

Morano, Eric↗

NASA NTRS1993

Parametric binary dissection

Binary dissection is widely used to partition non-uniform domains over parallel computers. This algorithm does not consider the perimeter, surface area, or aspect ratio of the regions being generated and can yield decompositions that have poor communication to computation ratio. Parametric Binary Dissection (PBD) is a new algorithm in which each cut is chosen to minimize load + lambda x(shape). In a 2 (or 3) dimensional problem, load is the amount of computation to be performed in a subregion and shape could refer to the perimeter (respectively surface) of that subregion. Shape is a measure of communication overhead and the parameter permits us to trade off load imbalance against communication overhead. When A is zero, the algorithm reduces to plain binary dissection. This algorithm can be used to partition graphs embedded in 2 or 3-d. Load is the number of nodes in a subregion, shape the number of edges that leave that subregion, and lambda the ratio of time to communicate over an edge to the time to compute at a node. An algorithm is presented that finds the depth d parametric dissection of an embedded graph with n vertices and e edges in O(max(n log n, de)) time, which is an improvement over the O(dn log n) time of plain binary dissection. Parallel versions of this algorithm are also presented; the best of these requires O((n/p) log(sup 3)p) time on a p processor hypercube, assuming graphs of bounded degree. How PBD is applied to 3-d unstructured meshes and yields partitions that are better than those obtained by plain dissection is described. Its application to the color image quantization problem is also discussed, in which samples in a high-resolution color space are mapped onto a lower resolution space in a way that minimizes the color error.

Bokhari, Shahid H.↗

NASA NTRS1993

A hybrid finite element-boundary integral for the analysis of cavity-backed antennas of arbitrary shape

This is the final report on this project which was concerned with the analysis of cavity-backed antennas and more specifically spiral antennas. The project was a continuation of a previous analysis, which employed rectangular brick elements, and was, thus, restricted to planar rectangular patch antennas. A total of five reports were submitted under this project and we expect that at least four journal papers will result from the research described in these reports. The abstracts of the four previous reports are included. The first of the reports (028918-1-T) is over 75 pages and describes the general formulation using tetrahedral elements and the computer program. Report 028918-2-T was written after the completion of the computer program and reviews the capability of the analysis and associated software for planar circular rectangular patches and for a rectangular planar spiral. Measurements were also done at the University of Michigan and at Mission Research Corp. for the purpose of validating the software. We are pleased to acknowledge a partial support from Mission Research Corp. in carrying out the work described in this report. The third report (028918-3-T) describes the formulation and partial validation (using 2D data) for patch antennas on a circular platform. The 3D validation and development of the formulation for patch antennas on circular platforms is still in progress. The fourth report (028918-4-T) is basically an invited journal paper which will appear in the 'J. Electromagnetic Waves and Applications' in early 1994. It describes the application of the finite element method in electromagnetics and is primarily based on our work here at U-M. This final report describes the culmination of our efforts in characterizing complex cavity-backed antennas on planar platforms. The report describes for the first time the analysis of non-planar spirals and non-rectangular slot antennas as well as traditional planar patch antennas. The comparisons between measurements and calculations are truly impressive. Another unique aspect of this work is the incorporation of the FFT as part of the BiCG solver by overlaying a structured triangular mesh over the unstructured mesh. The implementation of this BiCG-FFT solution algorithm is important in minimizing the CPU and storage requirements. This final report will be submitted for publication in a refereed journal.

Gong, Jian↗

NASA NTRS1992

Images constructed from computed flow fields

A method for constructing interferograms, schlieren, and shadowgraphs from ideal- and real-gas, two- and three-dimensional computed flow fields is described. The computational grids can be structured or unstructured, and multiple grids are an option. The constructed images are compared to experimental images for several types of flow, including a ramp, a blunt-body, a nozzle, and a reacting flow. The constructed images simulate the features observed in the experimental images. They are sensitive to errors in the flow-field solutions and can be used to identify solution errors. In addition, techniques for obtaining phase shifts from experimental finite-fringe interferograms and for removing experimentally induced phase-shift errors are discussed. Both the constructed images and calculated phase shifts can be used for validation of computational fluid dynamics (CFD) codes.

Yates, Leslie A.↗

NASA NTRS1993

Looking for O(N) Navier-Stokes solutions on non-structured meshes

Multigrid methods are good candidates for the resolution of the system arising in Numerical Fluid Dynamics. However, the question is to know if those algorithms which are efficient for the Poissan equation on structured meshes will still apply well to the Euler and Navier-Stokes equations on unstructured meshes. The study of elliptic problems leads us to define the conditions where a Full Multigrid strategy has O(N) complexity. The aim of this paper is to build a comparison between the elliptic theory and practical CFD problems. First, as an introduction, we will recall some basic definitions and theorems applied to a model problem. The goal of this section is to point out the different properties that we need to produce an FMG algorithm with O(N) complexity. Then, we will show how we can apply this theory to the fluid dynamics equations such as Euler and Navier-Stokes equations. At last, we present some results which are 2nd-order accurate and some explanations about the behavior of the FMG process.

Morano, Eric↗

NASA NTRS1993

An advancing-front Delaunay-triangulation algorithm designed for robustness

The following topics, which are associated with computational fluid dynamics, are discussed: unstructured mesh generation; the advancing front methodology; failures of the advancing front methodology; Delaunay triangulation; the Tanamua-Merriam algorithm; Yet Another Grid Generator (YAGG); and advancing front-Delaunay triangulation. The discussion is presented in viewgraph form.

D J Mavriplis↗

NASA NTRS1993

Dynamic mesh adaption for triangular and tetrahedral grids

The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

Rupak Biswas↗

NASA NTRS1993

Experience with parametric binary dissection

Parametric Binary Dissection (PBD) is a new algorithm that can be used for partitioning graphs embedded in 2- or 3-dimensional space. It partitions explicitly on the basis of nodes + (lambda)x(edges cut), where lambda is the ratio of time to communicate over an edge to the time to compute at a node. The new algorithm is faster than the original binary dissection algorithm and attempts to obtain better partitions than the older algorithm, which only takes nodes into account. The performance of parametric dissection with plain binary dissection on 3 large unstructured 3-d meshes obtained from computational fluid dynamics and on 2 random graphs were compared. It was showm that the new algorithm can usually yield partitions that are substantially superior, but that its performance is heavily dependent on the input data.

Bokhari, Shahid H.↗

NASA NTRS1993

A multilevel adaptive projection method for unsteady incompressible flow

There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.

Howell, Louis H.↗

NASA NTRS1993

Techniques and resources for storm-scale numerical weather prediction

The topics discussed include the following: multiscale application of the 5th-generation PSU/NCAR mesoscale model, the coupling of nonhydrostatic atmospheric and hydrostatic ocean models for air-sea interaction studies; a numerical simulation of cloud formation over complex topography; adaptive grid simulations of convection; an unstructured grid, nonhydrostatic meso/cloud scale model; efficient mesoscale modeling for multiple scales using variable resolution; initialization of cloud-scale models with Doppler radar data; and making effective use of future computing architectures, networks, and visualization software.

Droegemeier, Kelvin↗

NASA NTRS1993

Evaluation of computer-aided instruction techniques for the crew interface coordination position

The Crew Interface Coordinator (CIC) is responsible for real-time voice and procedural communication between the payload crew on the orbiter and the payload operations team on the ground. This function is dedicated to science activities and operations, and may also include some responsibilities for crew training. CIC training at Marshall Space Flight Center (MSFC) consists of mission-independent training, mission simulations, and line-organization training. As identified by Schneider, the program provides very good generic training; however position-specific training may be obtained in a very unstructured way. A computer-based training system, identified as Mac CIC, is currently under development to address this issue. Mac CIC is intended to provide an intermediate level of training in order to prepare the CIC for the more intensive mission simulations. Although originally intended as an intelligent tutoring system, Mac CIC currently exists as a hypertext-based application. The objectives of this research is to evaluate the current system and to provide both recommendations and a detailed plan for Mac CIC's evolution into an intelligent tutoring system.

Moynihan, Gary P.↗