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NASA NTRS1995

Numerical magetohydrodynamics in astronphysics: Algorithm and tests for one-dimensional flow`

We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.

Ryu, Dongsu↗

NASA NTRS1994

Numerical study of the wave-vector dependence of the electron interband impact ionization rate in bulk GaAs

Ensemble Monte Carlo calculations of the electron interband impact ionization rate in bulk GaAs are presented using a wave-vector (k)-dependent formulation of the ionization transition rate. The transition rate is evaluated through the use of numerically generated wavefunctions determined via a k-p calculation within the first two conduction bands at numerous points within a finely spaced three-dimensional grid in k space. The transition rate is determined to be greatest for states within the second conduction band. Is is found that the interband impact ionization transition rate in bulk GaAs is best characterized as having an exceedingly soft threshold energy. As a consequence, the dead space, defined as the distance over which the ionization probability for a given carrier is assumed to be zero, is estimated to be much larger than that estimated using a harder threshold. These results have importance in the design of the multiquantum-well avalanche photodiodes.

Wang, Yang↗

NASA NTRS1994

Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains

We use a combination of analytical and numerical methods to investigate the dynamics of charged dust grains in planetary magnetospheres. Our emphasis is on obtaining results valid for particles that are not necessarily dominated either by gravitational or electromagnetic forces. A Hamiltonian formulation of the problem yields exact results, for all values of charge-to-mass ratio, when we introduce two constraints: particles remain in the equatorial plane and the magnetic field is taken as axially symmetric. In particular, we obtain locations of equilibrium points, the frequencies of stable periodic orbits, the topology of separatrices in phase space, and the rate of longitudinal drift. These results are significant for specific applications: motion in the nearly aligned dipolar field of Saturn, and the trajectories of arbitrarily charged particles in complex magnetic fields for limited periods of time after ejection from parent bodies. Since the model is restrictive, we also use numerical integrations of the full three-dimensional equations of motion and illustrate under what conditions the constrained problem yields reasonable results. We show that a large fraction of the intermediately charged and highly charged (gyrating) particles will always be lost to a planet's atmosphere within a few hundred hours, for motion through tilted-dipole magnetic fields. We find that grains must have a very high charge-to-mass ratio in order to be mirrored back to the ring plane. Thus, except perhaps at Saturn where the dipole tilt is very small, the likely inhabitants of the dusty ring systems are those particles that are either nearly Keplerian (weakly charged) grains or grains whose charges place them in the lower end of the intermediate charge zone. Fianlly, we demonstrate the effect of plasma drag on the orbits of gyrating particles to be a rapid decrease in gyroradius followed by a slow radial evolution of the guiding center.

Schaffer, L.↗

NASA NTRS1994

Post-Gondwana geomorphic evolution of southwestern Africa: Implications for hte controls on landscape development from observations and numerical experiments

The relationship between morphology and surficial geology is used to quantify the denudation that has occurred across southwestern Africa sicne the fragmentation of Gondwana during the Early Mesozoic. Two main points emerge. Signficant denudation, of the order of kilometers, is widespread except in the Kalahari region of the continental interior. The denudation is systematically distributed so that the continental exterior catchment, draining directly to the Cape basin, is denuded to a greater depth than the interior catchment inland of the Great Escarpment. The analysis also implies tha the majority of the denudation occurred before the beginning of the Cenozoic for both teh exerior and interior catchments. Existing models of landscape development are reviewed, and implications of the denudation chronology are incorporated into a revised conceptual model. This revision implies tha thte primary effect of rifting on the subsequent landscape evolution is that it generates two distinct drainage regimes. A marginal upwarp, or rift flank uplift, separates rejuvenated rivers that drain into the subsiding rift from rivers in the continetal interior that are deflected but not rejuvenated. The two catchments evolve independently unless they are integrated by breaching of hte marginal upwarp. If this occurs, the exterior baselevel is communicated to the interior catchment that is denuded accordingly. Denudation rates generally decrease as the margin evolves, and this decrease is reinforced by the exposure of substrate that is resistant to denudation and/or a change to a more arid climate. The observations do not reveal a particular style of smaller-scale landscape evolution, sucha s escarpment retreat, that is responsible for the differential denudation across the region. It is proposed that numerical model experiments, which reflect the observational insights at the large scale, may identify the smaller-scale controls on escarpment development if the model and natural systems are analogous. Four numerical experiments are presented in which the roles of antecedent topography, resistant substrate, climte change, and lowering the baselevel of the interior catchment are investigated for an initially high elevation margin bordered by an escarpment. The model results suggest several styles of landscape evolution that are compatible with the observations. Escarpments may retreat in a regular manner, but they also degrade and are destroyed, only to reform at the drainage divide between exterior and interior catchments.

Gilchrist, Alan R.↗

NASA NTRS1994

Numerical simulation of three-dimensional self-gravitating flow

The three-dimensional flow of a self-gravitating fluid is numerically simulated using a Fourier pseudospectral method with a logarithmic variable formulation. Two cases with zero total angular momentum are studied in detail, a 32(exp 3) simulation (Run A) and a 64(exp 3) simulation (Run B). Other than the grid size, the primary differences between the two cases are that Run A modeled atomic hydrogen and had considerably more compressible motion initially than Run B, which modeled molecular hydrogen. ('Compressible motion' is that part of the velocity which has zero curl, but non-zero divergence). The numerical results indicate that gravitational collapse can proceed in a variety of ways. In Run A, collapse led to an elongated tube-like structure, while in Run B, collapse led to a flatter, disk-like structure.

Shebalin, J. V.↗

NASA NTRS1994

Experimental and numerical study of swept ramp injection into a supersonic flowfield

Time-averaged measurements of pressure, temperature, velocity, and injectant mole fraction are presented using the planar laser-induced iodine fluorescence technique in the complex three-dimensional compressible flowfield around a swept ramp fuel injector. Within the range of thermodynamic conditions present in the test case studied, the technique's accuracy is estimated to be 4% for pressure, temperature, and velocity and 3% for injectant mole fraction. Comparisons with numerical simulations using the SPARK three-dimensional Navier-Stokes computer code with an algebraic turbulence model are made at the centerplane of the flowfield as well as on three crossflow planes downstream of the injector. Calculations and measurements are in good agreement throughout the flowfield, with deviations on the order of 5%; however, in specific regions, such as in the base of the ramp, deviations are larger. A weak asymmetry in the incoming flowfield appears to be amplified by boundary-layer separation occurring when the ramp-generated shock reflects off the tunnel walls. Ramp-generated vortices are weaker in the calculated results due to the effects of numerical viscosity in the vortex cores. This leads to less turning and mixing of the jet plume than observed in the experiments. The rate of decay of the maximum injectant mole fraction with streamwise distance is greater for the present ramp injection scheme than for previously measured transverse injection schemes. In this recirculation region at the base of the injector, laminar calculations show better agreement with the measurements than turbulent calculations.

Donohue, James M.↗

NASA NTRS1992

Numerical study of multi-element airfoil aerodynamics

Unsteady flowfields around oscillating Boeing VR7 airfoil with and without a leading-edge slat were numerically investigated by a novel zonal method using a conformal mapping technique. Numerical aero-dynamic hysteresis loops show that the leading-edge slat prevents the airfoil dynamic stall at reduced frequency of 0.15, Reynolds number of 1 million, and the oscillation range of 5 deg to 25 deg.

Wang, Clin M.↗

NASA NTRS1995

Software For Numerical Simulation Of Geophysical Flows

Program verified by comparisons with both experimental and numerical studies. GEOSIM implements numerical model simulating geophysical fluid flow for wide range of problems. Allows for more accurate control over experimental conditions and provides complete data source for performing diagnostic studies. Used by experienced and/or professional fluid dynamicists. Written in FORTRAN 77.

Miller, Timothy L.↗

NASA NTRS1995

Observational and numerical studies of extreme frontal scale contraction

The general objective of this effort is to increase understanding of how frontal scale contraction processes may create and sustain intense mesoscale precipitation along intensifying cold fronts. The five-part project (an expansion of the originally proposed two-part project) employed conventional meteorological data, special mesoscale data, remote sensing measurements, and various numerical models. First an idealized hydrostatic modeling study of the scale contraction effects of differential cloud cover on low-level frontal structure and dynamics was completed and published in a peer-reviewed journal. The second objective was to complete and publish the results from a three dimensional numerical model simulation of a cold front in which differential sensible heating related to cloud coverage patterns was apparently crucial in the formation of a severe frontal squall line. The third objective was to use a nonhydrostatic model to examine the nonlinear interactions between the transverse circulation arising from inhomogeneous cloud cover, the adiabatic frontal circulation related to semi-geostrophic forcing, and diabatic effects related to precipitation processes, in the development of a density current-like microstructure at the leading edge of cold fronts. Although the development of a frontal model that could be used to initialize such a primitive equation model was begun, we decided to focus our efforts instead on a project that could be successfully completed in this short time, due to the lack of prospects for continued NASA funding beyond this first year (our proposal was not accepted for future funding). Thus, a fourth task was added, which was to use the nonhydrostatic model to test tentative hypotheses developed from the most detailed observations ever obtained on a density current (primarily sodar and wind profiler data). These simulations were successfully completed, the findings were reported at a scientific conference, and the results have recently been submitted to a peer-reviewed journal. The fifth objective was to complete the analysis of data collected during the Cooperative Oklahoma Profiler Studies (COPS-91) field project, which was supported by NASA. The analysis of the mesoscale surface and sounding data, Doppler radar imagery, and other remote sensing data from multi frequency wind profiler, microwave radiometer, and the Radio Acoustic Sounding System has been completed. This study is a unique investigation of processes that caused the contraction of a cold front to a microscale zone exhibiting an undular bore-like structure. Results were reported at a scientific conference and are being prepared for publication. In summary, considerable progress has been achieved under NASA funding in furthering our understanding of frontal scale contraction and density current - gravity wave interaction processes, and in utilizing models and remotely sensed data in such studies.

Koch, Steven E.↗

NASA NTRS1995

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Bui, Trong T.↗

NASA NTRS1995

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Krishnamoorthy, S.↗

NASA NTRS1995

Modeling and numerical simulation of microwave pulse propagation in air breakdown environment

It is shown that ionization occurs wherever the field intensity of the pulse exceeds the local breakdown threshold field of the background air. The produced plasma then attenuates the pulse and gives rise to a tail erosion phenomenon that plays the primary role in limiting the energy transfer of the pulse from source to destination. A theoretical model describing the propagation of an intense microwave pulse in an air breakdown environment is developed that includes the possible focusing effect introduced by either using phase array antennas or the other arrangements. The self-consistent description of the propagation process is provided by a set of two modal equations. These include a continuity equation (Poynting's equation) for the energy density of the pulse and a rate equation of the electron density. A forward wave approximation is used to simplify Poynting's equation, and a semiempirical formula is used for the ionization frequency, nu(sub i). This frequency provides the coupling between the two modal equations, and is used to express the electron rate equation explicitly. In terms of the relevant parameters of the atmosphere, these two equations are normalized for numerical analysis of pulse propagation in the atmosphere. The dependencies of the propagation characteristics of the pulse on intensity, frequency, width, and shape of the pulse are determined. The numerical simulations lead to a useful empirical relation p(exp 3)w = alpha = constant, where p and w are the incident power and width of the pulse and alpha depends on the percentage of pulse energy transferred from the source point to a destined position. The density distribution of the pulse's self-generated plasma is also evaluated. The results also show that for ionization caused by a single unfocused microwave pulse transmitted upwards from the ground, the maximum electron density produced at, for example, 50 km altitude is limited by the tail erosion effect to below 10(exp 6) cm(exp -3). Repetitive pulse and focused beam approaches are also examined. Both approaches can increase the maximum electron density by no more than an order of magnitude. A scheme using two obliquely propagating pulses intersecting at the destined height, e.g. 50 km, is considered. It is shown that the electron density generated at the lowest intersecting position can easily reach a value of 6.6 x 10(exp 8) cm(exp -3), which is considered to be high enough for artificial ionospheric mirror (AIM) application.

Kim, J.↗

NASA NTRS1995

Implementation of a multiblock sensitivity analysis method in numerical aerodynamic shape optimization

A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.

Lacasse, James M.↗

NASA NTRS1995

Development of a Prototype Simulation Executive with Zooming in the Numerical Propulsion System Simulation

A major difficulty in designing aeropropulsion systems is that of identifying and understanding the interactions between the separate engine components and disciplines (e.g., fluid mechanics, structural mechanics, heat transfer, material properties, etc.). The traditional analysis approach is to decompose the system into separate components with the interaction between components being evaluated by the application of each of the single disciplines in a sequential manner. Here, one discipline uses information from the calculation of another discipline to determine the effects of component coupling. This approach, however, may not properly identify the consequences of these effects during the design phase, leaving the interactions to be discovered and evaluated during engine testing. This contributes to the time and cost of developing new propulsion systems as, typically, several design-build-test cycles are needed to fully identify multidisciplinary effects and reach the desired system performance. The alternative to sequential isolated component analysis is to use multidisciplinary coupling at a more fundamental level. This approach has been made more plausible due to recent advancements in computation simulation along with application of concurrent engineering concepts. Computer simulation systems designed to provide an environment which is capable of integrating the various disciplines into a single simulation system have been proposed and are currently being developed. One such system is being developed by the Numerical Propulsion System Simulation (NPSS) project. The NPSS project, being developed at the Interdisciplinary Technology Office at the NASA Lewis Research Center is a 'numerical test cell' designed to provide for comprehensive computational design and analysis of aerospace propulsion systems. It will provide multi-disciplinary analyses on a variety of computational platforms, and a user-interface consisting of expert systems, data base management and visualization tools, to allow the designer to investigate the complex interactions inherent in these systems. An interactive programming software system, known as the Application Visualization System (AVS), was utilized for the development of the propulsion system simulation. The modularity of this system provides the ability to couple propulsion system components, as well as disciplines, and provides for the ability to integrate existing, well established analysis codes into the overall system simulation. This feature allows the user to customize the simulation model by inserting desired analysis codes. The prototypical simulation environment for multidisciplinary analysis, called Turbofan Engine System Simulation (TESS), which incorporates many of the characteristics of the simulation environment proposed herein, is detailed.

Reed, John A.↗

NASA NTRS1995

Direct Numerical Simulation of Transitional and Turbulent Flow Over a Heated Flat Plate Using Finite-Difference Schemes

The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.

Madavan, Nateri K.↗

NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Ponenti, Pj.↗

NASA NTRS1995

Numerical Study of Boundary Layer Interaction with Shocks: Method Improvement and Test Computation

The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.

Adams, N. A.↗