SEARCH · Engineering Papers

Results for “CONSERVATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,027 records · Page 57

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the source terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗

NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗

NASA NTRS1986

Breakdown of the conservative potential equation

The breakdown of the conservative potential approximation occurs for all the airfoils tested. It develops as soon as the shock waves appear in the flow field. Since shock waves are not properly represented by the potential approximation, it is conjectured that the breakdown is due to the isentropic shock jump condition of the potential approximation.

Salas, M. D.↗

NASA NTRS1988

A study of numerical methods for hyperbolic conservation laws with stiff source terms

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by using implicit methods, but other numerical difficulties are observed. The behavior of typical numerical methods on a simple advection equation with a parameter-dependent source term was studied. Two approaches to incorporate the source term were utilized: MacCormack type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. Various comparisons over a wide range of parameter values were made. In the stiff case where the solution contains discontinuities, incorrect numerical propagation speeds are observed with all of the methods considered. This phenomenon is studied and explained.

Leveque, R. J.↗

NASA NTRS1988

Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.

Abramopoulos, Frank↗

NASA NTRS1988

'Flux conservation' by a Schwarzschild gravitational lens

It is demonstrated, by an explicit calculation, that a single, isolated Schwarzschild gravitational lens leads to a vanishing net total amplification on its own, without any 'help' from other lenses. It is shown that, in the limit of small M/R (where M is the mass of the lens in geometrical units and R is the distance from the source to the observers), the positive net total amplification, obtained from the classical approximation of the amplification for small impact angle lensing, is balanced by a negative net total amplification from the first-order term in M/R in an approximation of the amplification for large impact angle lensing derived here. The relation of these results to the common interpretation of average flux conservation by gravitational lenses is discussed as due to the collective action of many lenses in a cosmological framework.

Shulami, I.↗

NASA NTRS1988

Non-oscillatory central differencing for hyperbolic conservation laws

Many of the recently developed high resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block for these schemes is the averaging of an appropriate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the direction of the wind. Instead, the use of the more robust Lax-Friedrichs (LxF) solver is proposed. The main advantage is simplicity: no Riemann problems are solved and hence field-by-field decompositions are avoided. The main disadvantage is the excessive numerical viscosity typical to the LxF solver. This is compensated for by using high-resolution MUSCL-type interpolants. Numerical experiments show that the quality of results obtained by such convenient central differencing is comparable with those of the upwind schemes.

Nessyahu, Haim↗

NASA NTRS1988

Some observations on boundary conditions for numerical conservation laws

Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

Kamowitz, David↗

NASA NTRS1989

Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium

The conservation equations for simulating hypersonic flows in thermal and chemical nonequilibrium and details of the associated physical models are presented. These details include the curve fits used for defining thermodynamic properties of the 11 species air model, curve fits for collision cross sections, expressions for transport properties, the chemical kinetics models, and the vibrational and electronic energy relaxation models. The expressions are formulated in the context of either a two or three temperature model. Greater emphasis is placed on the two temperature model in which it is assumed that the translational and rotational energy models are in equilibrium at the translational temperature, T, and the vibrational, electronic, and electron translational energy modes are in equilibrium at the vibrational temperature, T sub v. The eigenvalues and eigenvectors associated with the Jacobian of the flux vector are also presented in order to accommodate the upwind based numerical solutions of the complete equation set.

Peter A. Gnoffo↗

NASA NTRS1989

Second-order accurate nonoscillatory schemes for scalar conservation laws

Explicit finite difference schemes for the computation of weak solutions of nonlinear scalar conservation laws is presented and analyzed. These schemes are uniformly second-order accurate and nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time.

Huynh, Hung T.↗

NASA NTRS1988

A sufficient condition for the stability of conservative gyroscopic systems

A sufficient condition for the stability of conservative gyroscopic systems with negative definite stiffness is presented. The conditions for stability are stated in terms of the definiteness of certain combinations of the coefficient matrices of the equations of motion. These conditions yield design constraints in terms of the physical parameters of the system. An example is given to illustrate the correctness of the results, as well as to provide a comparison with the results of other researchers.

Inman, D. J.↗

NASA NTRS1989

Universal limiter for high order explicit conservative advection schemes

A simple method for construction of nonoscillatory, explicit, conservative advection schemes of arbitrarily high accuracy is described. Four test profiles are considered: an isolated sine-squared wave, a unit step function, a semiellipse, and a narrow Gaussian. A universal limiter guarantees monotonic resolution of the step. Sharpness increases uniformly with the order of the base scheme.

Leonard, B. P.↗

NASA NTRS1989

Ozone conservation and entrainment in cumulus congestus

This study demonstrates that ozone mixing ratio is conserved during moist convection and can be used as a tracer for cloud entrainment studies. The approach is to apply mixing line analysis to pairs of liquid water potential temperature, total water mixing ratio, O3 and pseudo-equivalent potential temperature derived from aircraft penetrations of growing cumulus congestus. Conclusions about entrainment from the mixing diagrams employing O3 agree with those using thermodynamic quantities. Any disagreement uncovered deficiencies in the water substance measurement technique.

Pearson, R., Jr.↗

NASA NTRS1990

Triangle based TVD schemes for hyperbolic conservation laws

A triangle based total variation diminishing (TVD) scheme for the numerical approximation of hyperbolic conservation laws in two space dimensions is constructed. The novelty of the scheme lies in the nature of the preprocessing of the cell averaged data, which is accomplished via a nearest neighbor linear interpolation followed by a slope limiting procedures. Two such limiting procedures are suggested. The resulting method is considerably more simple than other triangle based non-oscillatory approximations which, like this scheme, approximate the flux up to second order accuracy. Numerical results for linear advection and Burgers' equation are presented.

Durlofsky, Louis J.↗

NASA NTRS1990

High order filtering methods for approximating hyberbolic systems of conservation laws

In the computation of discontinuous solutions of hyperbolic systems of conservation laws, the recently developed essentially non-oscillatory (ENO) schemes appear to be very useful. However, they are computationally costly compared to simple central difference methods. A filtering method which is developed uses simple central differencing of arbitrarily high order accuracy, except when a novel local test indicates the development of spurious oscillations. At these points, the full ENO apparatus is used, maintaining the high order of accuracy, but removing spurious oscillations. Numerical results indicate the success of the method. High order of accuracy was obtained in regions of smooth flow without spurious oscillations for a wide range of problems and a significant speed up of generally a factor of almost three over the full ENO method.

Lafon, F.↗

NASA NTRS1990

The cost of conservative synchronization in parallel discrete event simulations

The performance of a synchronous conservative parallel discrete-event simulation protocol is analyzed. The class of simulation models considered is oriented around a physical domain and possesses a limited ability to predict future behavior. A stochastic model is used to show that as the volume of simulation activity in the model increases relative to a fixed architecture, the complexity of the average per-event overhead due to synchronization, event list manipulation, lookahead calculations, and processor idle time approach the complexity of the average per-event overhead of a serial simulation. The method is therefore within a constant factor of optimal. The analysis demonstrates that on large problems--those for which parallel processing is ideally suited--there is often enough parallel workload so that processors are not usually idle. The viability of the method is also demonstrated empirically, showing how good performance is achieved on large problems using a thirty-two node Intel iPSC/2 distributed memory multiprocessor.

Nicol, David M.↗

NASA NTRS1989

Conservation of body calcium by increased dietary intake of potassium: A potential measure to reduce the osteoporosis process during prolonged exposure to microgravity

During the 1988 NASA Summer Faculty Fellowship Program, it was proposed that the loss of skeletal calcium upon prolonged exposure to microgravity could be explained, in part, by a renal maladjustment characterized by an increased urinary excretion of calcium. It was theorized that because the conservation of body fluids and electrolytes depends upon the energy of adenosine triphosphate and enzymes that control the use of its energy for renal ion transport, an induction of renal sodium and potassium-dependent adenosine triphosphatase (Na + K ATPase) by oral loading with potassium would increase the reabsorption of sodium directly and that of calcium indirectly, leading to improved hydration and to reduced calcium loss. Preliminary studies showed the following. Rats drinking water containing 0.2 M potassium chloride for six to 13 days excreted in urine 22 muEq of calcium and 135 muEq of sodium per 100 grams of body weight per day. The corresponding values for control rats drinking tap water were 43 muEq and 269 muEq respectively. Renal Na + K ATPase activity in potassium loaded rats was higher than in controls. Thus, oral potassium loading resulted in increased Na + K ATPase activity and diminished urinary excretion of calcium and of sodium as predicted by the hypothesis. An extension of these studies to humans has the potential of resulting in development of harmless, non-invasive, drug-free, convenient measures to reduce bone loss and other electrolyte and fluid problems in space travelers exposed to prolonged periods of microgravity.

Nechay, Bohdan R.↗

NASA NTRS1990

Numerical methods for systems of conservation laws of mixed type using flux splitting

The essentially non-oscillatory (ENO) finite difference scheme is applied to systems of conservation laws of mixed hyperbolic-elliptic type. A flux splitting, with the corresponding Jacobi matrices having real and positive/negative eigenvalues, is used. The hyperbolic ENO operator is applied separately. The scheme is numerically tested on the van der Waals equation in fluid dynamics. Convergence was observed with good resolution to weak solutions for various Riemann problems, which are then numerically checked to be admissible as the viscosity-capillarity limits. The interesting phenomena of the shrinking of elliptic regions if they are present in the initial conditions were also observed.

Shu, Chi-Wang↗