SEARCH · Search NASA

Results for “CONSERVATION LAW”

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 253 records · Page 14

All sources NASA NTRS DOE OSTI

NASA NTRS1981

An analytic treatment of the structure of the bow shock and magnetosheath

A theoretical examination of the jump conditions of the bow shock is used to investigate the influence of the solar wind magnetic fields on the structure of the parameters behind the bow shock. Through the assumption that the average values of the parameters along the radial direction in the magnetosheath are equal to their values just behind the bow shock, the influence of the direction of the solar wind magnetic fields on the average structure of the magnetosheath is determined. From this assumption, a zero-order formula for the thickness of the magnetosheath is deduced which satisfies the boundary conditions and conservation laws of mass and momentum flux. The theoretical estimate of the thickness is compared with satellite observations to check the assumption and select the optimum value of the polytropic exponent of the plasma gas.

Zhuang, H. C.↗

NASA NTRS1981

Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Steger, J. L.↗

NASA NTRS1981

Stable boundary approximations for a class of implicit schemes for the one-dimensional inviscid equations of gas dynamics

The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.

Yee, H. C.↗

NASA NTRS1981

Computation of simple three-dimensional wing-vortex interaction in transonic flow

An implicit delta form finite-difference algorithm for Euler equations in conservation law form has been used in preliminary calculations of three-dimensional wing-vortex interactions. Both steady and unsteady transonic flow wing-vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two- and three-dimensions.

Srinivasan, G. R.↗

NASA NTRS1981

Computation of wing-vortex interaction in transonic flow using implicit finite difference algorithm

An implicit delta form finite difference algorithm for Euler equations in conservation law form was used in preliminary calculations of three dimensional wing vortex interaction. Both steady and unsteady transonic flow wing vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two and three dimensions. Combination of these methods can reduce the overall computational time by a factor of 4.

Srinivasan, G.↗

NASA NTRS1982

Mechanics of couple-stress fluid coatings

The formal development of a theory of viscoelastic surface fluids with bending resistance - their kinematics, dynamics, and rheology are discussed. It is relevant to the mechanics of fluid drops and jets coated by a thin layer of immiscible fluid with rather general rheology. This approach unifies the hydrodynamics of two-dimensional fluids with the mechanics of an elastic shell in the spirit of a Cosserat continuum. There are three distinct facets to the formulation of surface continuum mechanics. Outlined are the important ideas and results associated with each: the kinematics of evolving surface geometries, the conservation laws governing the mechanics of surface continua, and the rheological equations of state governing the surface stress and moment tensors.

Waxman, A. M.↗

NASA NTRS1981

Creep crack-growth: A new path-independent T sub o and computational studies

Two path independent integral parameters which show some degree of promise as fracture criteria are the C* and delta T sub c integrals. The mathematical aspects of these parameters are reviewed. This is accomplished by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects and large deformations. Two principal conclusions are that delta T sub c is a valid crack tip parameter during nonsteady as well as steady state creep and that delta T sub c has an energy rate interpretation whereas C* does not. An efficient, small displacement, infinitestimal strain, displacement based finite element model is developed for general elastic/plastic material behavior. For the numerical studies, this model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations.

Stonesifer, R. B.↗

NASA NTRS1981

Analysis of cracks emanating from a circular hole in unidirectional fiber reinforced composites, part 2

An analytical method is developed for cracks emanating from a circular hole in an off-axis unidirectional fiber-reinforced composite. The method which is formulated by using conservation laws of elasticity and fundamental relationships in anisotropic fracture mechanics, provides a convenient and accurate means to examine the complicated crack behavior, when used in conjunction with a suitable numerical scheme such as the finite element method. The formulation is eventually reduced to a system of linear algebraic equations of mixed-mode stress intensity factors. Fracture parameters, describing crack-tip deformation and fracture in the composite, are obtained explicitly. Effects of material anisotropy and crack/hole geometry are examined also. Of particular interest are the energy release rates associated with crack extension; their values are evaluated for various cases. Results show that mixed-mode stress intensity factors and energy release rates associated with the cracks emanating from a hole change very appreciably with fiber orientation in the composite. K sub 1 and G increase monotonically with increasing theta; but K sub 2 reaches its maximum at theta = 45 deg, and then decreases gradually as theta increases further.

Wang, S. S.↗

NASA NTRS1981

Analysis of interface cracks in adhesively bonded lap shear joints, part 4

Conservation laws of elasticity for nonhomogeneous materials were developed and were used to study the crack behavior in adhesively bonded lap shear joints. By using these laws and the fundamental relationships in fracture mechanics of interface cracks, the problem is reduced to a pair of linear algebraic equations, and stress intensity solutions can be determined directly by information extracted from the far field. The numerical results obtained show that: (1) in the lap-shear joint with a given adherend, the opening-mode stress intensity factor, (K sub 1) is always larger than that of the shearing-mode (K sub 2); (2) (K sub 1) is not sensitive to adherent thickness abut (K sub 2) increases rapidly with increasing thickness; and (3) (K sub 1) and (K sub 2) increase simultaneously as the interfacial crack length increases.

Wang, S. S.↗

NASA NTRS1982

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator.

Yee, H. C.↗

NASA NTRS1982

Creep crack-growth: A new path-independent integral (T sub c), and computational studies

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Stonesifer, R. B.↗

NASA NTRS1982

Computations of transonic flow over an oscillating airfoil with shock-induced separation

A numerical study is presented on unsteady transonic flow over an airfoil in pitching oscillation at a moderately high incidence. The study was focused on the effects of unsteady shock-wave/boundary-layer interactions and subsequent flow separations. An implicit finite-difference scheme was used to solve the full time-dependent compressible Navier-Stokes equations in conservation-law form. The algorithm adopted for this study is the Beam-Warming spatially factored scheme. It is, however, constructed in a body-fitted curvilinear coordinate system for efficient unsteady flow computations. The computational results are compared with experimental data measured in the Ames 11- by 11-Foot Transonic Wind Tunnel.

Chyu, W. J.↗

NASA NTRS1982

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Bridgeman, J. O.↗

NASA NTRS1982

Interface cracks in adhesively bounded lap-shear joints

A study on the elastic behavior of interface cracks in adhesively bonded lap-shear joints is presented. The problem is investigated by using a recently developed method of analysis based on conservation laws in elasticity for nonhomogeneous solids and fundamental relationships in fracture mechanics of dissimilar materials. The formulation leads to a pair of linear algebraic equations in mixed-mode stress intensity factors. Singular crack-tip stress intensity solutions are determined directly by information extracted from the far field. Stress intensity factors and associated energy release rates are obtained for various cases of interest. Fundamental nature of the interfacial flaw behavior in lap-shear adhesive joints is examined in detail.

Wang, S. S.↗

NASA NTRS1982

Electrostriction in liquid He-4

The two-fluid model of liquid He-4 is extended to include effects of applied electric fields. New terms that account for electrostriction in equations of motion for superfluid and normal fluid are derived with the aid of a variational principle subject to the assumption that the Clausius-Mossotti relation for the dielectric constant is applicable. Corresponding additions to conservation laws for momentum and energy are presented.

Jackson, H. W.↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

The large-time behavior of the scalar, genuinely nonlinear Lax-Friedrichs scheme

The Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u sub t + f sub x (u) = 0 where f(u) is, say, strictly convex double dot f dot a sub asterisk 0 is studied. The divided differences of the numerical solution at time t do not exceed 2 (t dot a sub asterisk) to the -1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in particular, it is independent of the initial amplitude in sharp contrast to liner problems. It guarantees the entropy compactness of the scheme in this case, as well as providing a quantitive insight into the large-time behavior of the numerical computation.

Tadmor, E.↗

NASA NTRS1983

Application of second-order-accurate Total Variation Diminishing (TVD) schemes to the Euler equations in general geometries

A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.

Yee, H. C.↗