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NASA NTRS1988

A conservative approach for flow field calculations on multiple grids

In the computation of flow fields about complex configurations, it is very difficult to construct body-fitted coordinate systems. An alternative approach is to use several grids at once, each of which is generated independently. This procedure is called the multiple grids or zonal grids approach and its applications are investigated in this study. The method follows the conservative approach and provides conservation of fluxes at grid interfaces. The Euler equations are solved numerically on such grids for various configurations. The numerical scheme used is the finite-volume technique with a three-state Runge-Kutta time integration. The code is vectorized and programmed to run on the CDC VPS-32 computer. Some steady state solutions of the Euler equations are presented and discussed.

Kathong, Monchai↗

NASA NTRS1989

Conserving approximations for strongly correlated electron systems - Bethe-Salpeter equation and dynamics for the two-dimensional Hubbard model

A semianalytical approach is described for strongly correlated electronic systems which satisfies microscopic conservation laws, treats strong frequency and momentum dependences, and provides information on both static and dynamic properties. This approach may be used to treat large systems and temperatures lower than those currently accessible to finite-temperature quantum Monte Carlo techniques. Examples of such systems include heavy-electron compounds, organic Bechegaard salts, bis-(ethylenedithiolo)-TTF superconductors, and the oxide superconductors. The technique is based on the derivation and self-consistent solution of infinite-order conserving approximations. The technique is used to derive a low-temperature phase diagram and dynamic correlation functions for the two-dimensional Hubbard lattice model.

Bickers, N. E.↗

NASA NTRS1989

Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations

Conservative algorithms for boundaray interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.

Moon, Young J.↗

NASA NTRS1989

On the application of subcell resolution to conservation laws with stiff source terms

LeVeque and Yee recently investigated a one-dimensional scalar conservation law with stiff source terms modeling the reacting flow problems and discovered that for the very stiff case most of the current finite difference methods developed for non-reacting flows would produce wrong solutions when there is a propagating discontinuity. A numerical scheme, essentially nonoscillatory/subcell resolution - characteristic direction (ENO/SRCD), is proposed for solving conservation laws with stiff source terms. This scheme is a modification of Harten's ENO scheme with subcell resolution, ENO/SR. The locations of the discontinuities and the characteristic directions are essential in the design. Strang's time-splitting method is used and time evolutions are done by advancing along the characteristics. Numerical experiment using this scheme shows excellent results on the model problem of LeVeque and Yee. Comparisons of the results of ENO, ENO/SR, and ENO/SRCD are also presented.

Chang, Shih-Hung↗

NASA NTRS1990

A kinetic equation with kinetic entropy functions for scalar conservation laws

A nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws. In particular, it is proved to be well-posed uniformly in epsilon - the microscopic scale. It is also shown that the proposed kinetic equation is equipped with a family of kinetic entropy functions - analogous to Boltzmann's microscopic H-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, it is proved by both - BV compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with epsilon below 0 to the unique entropy solution of the corresponding conservation law.

Perthame, Benoit↗

NASA NTRS1990

Conservative buffering of approximate nonlinear constraints

In engineering design practice behavior is usually predicted based on some known nominal design. However, when the design is fabricated it will differ from the nominal design because of manufacturing tolerances. In order to generate nominal designs that will still satisfy behavior constraints in the presence of manufacturing tolerances, engineers resort to the use of safety factors, over and above those introduced to account for other uncertainties (e.g., in load conditions, material properties, analysis modeling). The accurate selection of the values of these manufacturing tolerances safety factors is dependent on the capability of the engineer to determine the sensitivity of the critical constraints to changes in the design variables. This process usually leads to overly conservative designs. The task of choosing safety factors is much more difficult in structural synthesis because: (1) it is not known which constraints will be active at the final design, (2) as the design changes during the synthesis process the sensitivities of the constraints with respect to the design variables also change, and (3) the imposition of the safety factors themselves may change the set of critical constraints. These difficulties can be overcome with the approximation concepts approach to structural synthesis by buffering the approximate constraints with quantities that are related to the design variable tolerances and the accurate sensitivities of the constraints with respect to the design variable. Designs generated by this approach tend to be feasible but not overly conservative.

Thomas, H. L.↗

NASA NTRS1990

Conservative parallel simulation of priority class queueing networks

A conservative synchronization protocol is described for the parallel simulation of queueing networks having C job priority classes, where a job's class is fixed. This problem has long vexed designers of conservative synchronization protocols because of its seemingly poor ability to compute lookahead: the time of the next departure. For, a job in service having low priority can be preempted at any time by an arrival having higher priority and an arbitrarily small service time. The solution is to skew the event generation activity so that the events for higher priority jobs are generated farther ahead in simulated time than lower priority jobs. Thus, when a lower priority job enters service for the first time, all the higher priority jobs that may preempt it are already known and the job's departure time can be exactly predicted. Finally, the protocol was analyzed and it was demonstrated that good performance can be expected on the simulation of large queueing networks.

Nicol, David M.↗

NASA NTRS1990

A conservative approach to parallelizing the Sharks World simulation

Parallelizing a benchmark problem for parallel simulation, the Sharks World, is described. The described solution is conservative, in the sense that no state information is saved, and no 'rollbacks' occur. The used approach illustrates both the principal advantage and principal disadvantage of conservative parallel simulation. The advantage is that by exploiting lookahead an approach was found that dramatically improves the serial execution time, and also achieves excellent speedups. The disadvantage is that if the model rules are changed in such a way that the lookahead is destroyed, it is difficult to modify the solution to accommodate the changes.

Nicol, David M.↗

NASA NTRS1992

Achieving spectrum conservation for the minimum-span and minimum-order frequency assignment problems

Effective and efficient solutions of frequency assignment problems assumes increasing importance as the radiofrequency spectrum experiences ever increasing utilization by diverse communications services, requiring that the most efficient use of this resource be achieved. The research presented explores a general approach to the frequency assignment problem, in which such problems are categorized by the appropriate spectrum conserving objective function, and are each treated as an N-job, M-machine scheduling problem appropriate for the objective. Results obtained and presented illustrate that such an approach presents an effective means of achieving spectrum conserving frequency assignments for communications systems in a variety of environments.

Heyward, Ann O.↗

NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗

NASA NTRS1992

Achieving spectrum conservation for the minimum span and minimum-order frequency assignment problems

Effective and efficient solution of frequency assignment problems assumes increasing importance as the radiofrequency spectrum experiences ever-increasing utilization by diverse communications services, requiring that the most efficient use of this resource be achieved. The research presented explores a general approach to the frequency assignment problem, in which such problems are categorized by the appropriate spectrum-conserving objective function, and are each treated as an N-job, M-machine scheduling problem appropriate for the objective. Results obtained and presented illustrate that such an approach presents an effective means of achieving spectrum-conserving frequency assignments for communications systems in a variety of environments.

Heyward, Ann O.↗

NASA NTRS1992

A discrete momentum-conserving explicit algorithm for multibody dynamics analysis

A discrete momentum-conserving, explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.

Park, K. C.↗

NASA NTRS1992

Conservative parallel simulation of priority class queueing networks

Nicol, David↗

NASA NTRS1993

Variable-Volume Flushing (V-VF) device for water conservation in toilets

Thirty five percent of residential indoor water used is flushed down the toilet. Five out of six flushes are for liquid waste only, which requires only a fraction of the water needed for solid waste. Designers of current low-flush toilets (3.5-gal. flush) and ultra-low-flush toilets (1.5-gal. flush) did not consider the vastly reduced amount of water needed to flush liquid waste versus solid waste. Consequently, these toilets are less practical than desired and can be improved upon for water conservation. This paper describes a variable-volume flushing (V-VF) device that is more reliable than the currently used flushing devices (it will not leak), is simple, more economical, and more water conserving (allowing one to choose the amount of water to use for flushing solid and liquid waste).

Jasper, Louis J., Jr.↗

NASA NTRS1992

Rhenium in seawater - Confirmation of generally conservative behavior

A depth profile of the concentration of Re was measured in the Pacific Ocean using a technique developed for the clean chemical separation and the precise measurement of Re by isotope dilution and negative thermal ionization mass spectrometry (ID-NTIMS). We obtain a narrow range for Re from 7.20 +/- 0.03 to 7.38 +/- 0.03 ng/kg for depths between 45 m and 4700 m. This demonstrates that Re is relatively well mixed throughout the water column and confirms the theoretical prediction that the behavior of Re in the oceans is conservative. When examined in detail, both salinity and the concentration of Re increase by approximately 1.5 percent between 400 and 4700 m, a correlation consistent with conservative behavior. However, Re appears to be depleted relative to salinity by 1.0-1.5 percent at 100 m, and enriched by approximately 4 percent at the surface. These observations suggest a minor level of Re scavenging in near surface waters, and an input of Re to the ocean surface. This work demonstrates the utility of geochemical investigations of certain trace elements not previously been amenable to detailed study.

Anbar, A. D.↗

NASA NTRS1993

Density-conserving shape factors for particle simulations in cylindrical and spherical coordinates

It is established that a particle-to-grid weighting which is based on both conventional particle-in-cell (PIC) and cloud-in-cell (CIC) shape factors will yield nonuniform grid densities, even in the case of uniform particle distributions, in both cylindrical and spherical coordinates. In view of this, alternative density-conserving weighting schemes are discussed which encompass modified PIC and CIC weighting. These alternative shape factors are mathematically no more complicated than the conventional nondensity-conserving expressions.

Ruyten, Wilhelmus M.↗

NASA NTRS1993

A discrete momentum-conserving explicit algorithm for rigid body dynamics analysis

A discrete momentum-conserving explicit time integration is presented. The accurate feature and simplicity of the present algorithm are realized by a mid-point implicit formula for integrating the Euler parameters and a second-order discrete momentum-conserving form of the central difference algorithm, respectively. The accuracy and robustness of the algorithm is demonstrated by example problems which exhibit large overall rigid motions under holonomic constraints.

Park, K. C.↗

NASA NTRS1990

On resonance in linear conservation laws without source terms

A phenomena is described occuring in wave propagation for systems of conservation laws which are not hyperbolic. The nature of the wave propagation for linear systems of conservation laws which are degenerate in the sense that they are not equivalent to diagonal systems is examined. It is concluded that in the degenerate case, 'resonance' occurs, that is, the solutions are combinations of traveling waves and 'resonance waves'. Here resonance means that the solution may become unbounded even if the initial values are bounded. The solutions (waves) can be described as a superposition of 'packets' (groups) of 'resonance waves' traveling with the same speed. These are linear systems with constant coefficients which are self-exciting, which is what one would expect to encounter in nonlinear systems.

Gingold, H.↗