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Finite difference method stability analysis of deformed eccentrically stiffened shells of revolution, accounting for finite prebuckling rotations
Report presents the finite difference equations in time and finite element matrix equations in space for general linear thermovisoelastic problems. The equations are derived for a general three-dimensional body but are applicable to one- and two-dimensional configurations with minor changes.
The containerless melting of high-purity multicomponent homogeneous gels and gel-monoliths offers a unique approach to making ultrapure multicomponent optical glasses in the reduced gravity environment of space. Procedures for preparing and characterizing gels and gel-derived glasses in the Na2O-B2O3-SiO2 system are described. Preparation is based on the polymerization reactions of alkoxysilane with trimethyl borate or boric acid and a suitable sodium compound. The chemistry of the gelling process is discussed in terms of process parameters and the gel compositions. The physicochemical nature of gels prepared by three different procedures were found to be significantly different. IR absorption spectra indicate finite differences in the molecular structures of the different gels. The melting of the gel powders and the transformation of porous gel-monoliths to transparent 'glass' without melting are described.
The containerless melting of high-purity multicomponent homogeneous gels and gel monoliths offers a unique approach to making ultrapure multicomponent optical glasses in the reduced gravity environment of space. Procedures for preparing and characterizing gels and gel-derived glasses in the system Na2O-B2O3-SiO2 are described. Preparation is based on the polymerization reactions of alkoxysilane with trimethyl borate or boric acid and a suitable sodium compound. The chemistry of the gelling process is discussed in terms of process parameters and the gel compositions. The physicochemical nature of gels prepared by three different procedures was found to be significantly different. Infrared absorption spectra indicate finite differences in the molecular structures of the different gels. The melting of the gel powders and the transformation of porous gel monoliths to transparent 'glass' without melting are described.
A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.
A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
The design complexity and size of convectively-cooled engine and airframe structures for hypersonic transports necessitate the use of large general purpose computer programs for both thermal and structural analyses. Generally thermal analyses are based on the lumped-parameter finite difference technique, and structural analyses are based on the finite element technique. Differences in these techniques make it difficult to achieve an efficient interface. It appears, therefore, desirable to conduct an integrated analysis based on a common technique. A summary is provided of efforts by NASA concerned with the development of an integrated thermal structural analysis capability using the finite element method. Particular attention is given to the development of conduction/forced-convection finite element methodology and applications which illustrate the capabilities of the developed concepts.
Mathematical treatment of nonstationary heat- conduction processes by applying finite differences in space and differentials in time
Inequalities for theory of finite difference equations and more general discontinuous functional equations
Equations for thin elastic spherical shells and digital program for analysis of stresses and deformation of fixed edge segmental spherical shells - solution by finite difference technique
Momentum and heat transfer in axisymmetric turbulent free jets exhausting into quiescent air, using finite difference technique
The stability of finite difference approximations to initial boundary hyperbolic systems is studied. As is well known, a proper specification of boundary conditions for such systems is essential for their solutions to be well defined. A discrete analogue of the above is proved - if the numerical boundary conditions are consistent with an inflow part of the problem, they render the overall computation unstable. An example of the inviscid gasdynamics equations is considered.
The stability of finite difference approximations to initial boundary hyperbolic systems is studied. As is well known, a proper specification of boundary conditions for such systems is essential for their solutions to be well defined. A discrete analogue of the above is proved - if the numerical boundary conditions are consistent with an inflow part of the problem, they render the overall computation unstable. An example of the inviscid gasdynamics equations is considered. Previously announced in STAR as N81-33874
A two dimensional finite difference thermal model was developed to predict the effects of heating profile, fill level, and cryogen type prior to experimental testing the Generic Research Cryogenic Tank (GRCT). These numerical predictions will assist in defining test scenarios, sensor locations, and venting requirements for the GRCT experimental tests. Boiloff rates, tank-wall and fluid temperatures, and wall heat fluxes were determined for 20 computational test cases. The test cases spanned three discrete fill levels and three heating profiles for hydrogen and nitrogen.
Surface flow and subsurface flow constitute a naturally linked hydrologic continuum that has not traditionally been simulated in an integrated fashion. Recognizing the interactions between these systems has encouraged the development of integrated hydrologic models (IHMs) capable of treating surface and subsurface systems as a single integrated resource. IHMs are dynamically evolving with improvements in technology, and the extent of their current capabilities are often only known to the developers and not general users. This article provides an overview of the core functionality, capability, applications, and ongoing development of one open-source IHM, ParFlow. ParFlow is a parallel, integrated, hydrologic model that simulates surface and subsurface flows. ParFlow solves the Richards equation for three-dimensional variably saturated groundwater flow and the two-dimensional kinematic wave approximation of the shallow water equations for overland flow. The model employs a conservative centered finite-difference scheme and a conservative finite-volume method for subsurface flow and transport, respectively. ParFlow uses multigrid-preconditioned Krylov and Newton–Krylov methods to solve the linear and nonlinear systems within each time step of the flow simulations. The code has demonstrated very efficient parallel solution capabilities. ParFlow has been coupled to geochemical reaction, land surface (e.g., the Common Land Model), and atmospheric models to study the interactions among the subsurface, land surface, and atmosphere systems across different spatial scales. This overview focuses on the current capabilities of the code, the core simulation engine, and the primary couplings of the subsurface model to other codes, taking a high-level perspective.
Finite difference method for solving symmetric positive linear differential equations
Finite difference methods using computer for boundary value problem of ionospheric electron density
Laminar tube flow and heat transfer for He gas using Navier-Stokes, energy and continuity equations in finite difference form