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At least 145 records · Page 8

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NASA NTRS1991

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Tamma, Kumar K.↗

NASA NTRS1991

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Walker, K. P.↗

NASA NTRS1986

Transonic potential flow in hyperbolic nozzles

The full potential equation for the classical problem of transonic flow through a hyperbolic nozzle (with or without a shock wave) is solved in conservation form using the finite volume method of Jameson and Caughey (1977). Either a firstor a second-order numerical viscosity is added in the direction of the flow, explicitly, in conservation form. A multigrid alternating direction implicit method is used to solve the difference equations, and the results obtained are compared with analytical and numerical results from previous researches.

Park, M.↗

NASA NTRS1991

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

Stremel, Paul M.↗

NASA NTRS1992

Computing high-speed flows past an oscillating cylinder near a vertical wall

A computational method to simulate unsteady flows involving moving rigid boundaries and interference has been developed. The method is used to solve inviscid equations governing the fluid flow and the dynamic equations governing the motion of rigid bodies. A second-order accurate, upwind-biased, and alterating-direction-implicit method is used to solve the governing equations of the flow. A kinematic domain decomposition (KDD) procedure is extended to treat 3D problems with a high degree of accuracy and generality. The method under consideration is applied to both transonic and supertransonic flows. Both cases involve flow past a cylinder which is forced to pitch sinusoidally near a vertical wall. Benefits of the proposed approach include accurate calculation of the flow around 3D moving multiple bodies with interference; reduction of a numerical error; in particular, the dispersion error which strongly affects wave propagation; and minimization of the phase error which is accumulated according to the time advance procedure.

Yen, Guan-Wei↗

NASA NTRS1987

Decoupled direct method for sensitivity analysis in combustion kinetics

An efficient, decoupled direct method for calculating the first order sensitivity coefficients of homogeneous, batch combustion kinetic rate equations is presented. In this method the ordinary differential equations for the sensitivity coefficients are solved separately from , but sequentially with, those describing the combustion chemistry. The ordinary differential equations for the thermochemical variables are solved using an efficient, implicit method (LSODE) that automatically selects the steplength and order for each solution step. The solution procedure for the sensitivity coefficients maintains accuracy and stability by using exactly the same steplengths and numerical approximations. The method computes sensitivity coefficients with respect to any combination of the initial values of the thermochemical variables and the three rate constant parameters for the chemical reactions. The method is illustrated by application to several simple problems and, where possible, comparisons are made with exact solutions and those obtained by other techniques.

Radhakrishnan, Krishnan↗

NASA NTRS1991

Computational methods for structural load and resistance modeling

An automated capability for computing structural reliability considering uncertainties in both load and resistance variables is presented. The computations are carried out using an automated Advanced Mean Value iteration algorithm (AMV +) with performance functions involving load and resistance variables obtained by both explicit and implicit methods. A complete description of the procedures used is given as well as several illustrative examples, verified by Monte Carlo Analysis. In particular, the computational methods described in the paper are shown to be quite accurate and efficient for a material nonlinear structure considering material damage as a function of several primitive random variables. The results show clearly the effectiveness of the algorithms for computing the reliability of large-scale structural systems with a maximum number of resolutions.

Thacker, B. H.↗

NASA NTRS2004

OTIS 3.2 Software Released

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

Riehl, John P.↗

NASA NTRS1978

Viscous flow analysis in mixed flow rotors

A method for analyzing the viscous flow through turbomachine rotors is presented. The field analysis is based upon the solution of the full Navier-Stokes equations over the rotor blade-to-blade stream channels. An Alternating-Direction-Implicit method is employed to carry out the necessary numerical integration of the elliptic governing equations. The flow analysis may be applied to various types of turbomachine rotors. Preliminarily, only the case of laminar flows are considered in this paper. The flow characteristics within the rotors of a mixed flow turbine and a radial bladed compressor are investigated over a wide range of operating conditions. Excellent results are obtained when compared with existing experimental data. The method of this analysis is quite general and can deal with a wide range of applications. Possible modification of the present study to deal with turbulent flow cases are also identified.

Khalil, I.↗

NASA NTRS1991

Unstructured-grid methods development: Lessons le arned

The development is summarized of unstructured grid methods for the solution of the equations of fluid flow and some of the lessons learned are shared. The 3-D Euler equations are solved, including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an upwind implicit method using a CFL (Courant Friedricks Lewy) number of infinity is presented for the Boeing 747 aircraft. The results obtained in less than one hour of CPU time on a Cray-2 computer, thus demonstrating the speed and robustness of the present capability.

Batina, John T.↗

NASA NTRS1980

Numerical methods for large-scale time-dependent partial differential equations

The factors that influence the choice of a numerical solution scheme for large-scale time-dependent partial differential equations are examined with emphasis on the treatment of boundaries. Consideration is given to standard boundary treatments, moving boundaries, and artificial boundaries simulating an infinite domain. Implicit methods and applications to specific problems are discussed with special attention to shocks and steady state solutions.

Turkel, E.↗

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

Computer modeling of convection in the liquid metal during solidification

Numerical methods are used to study thermally/gravitationally induced convection during solidification. The primary object is aimed at understanding the flow field in the liquid metal pool due to convection. An Al-0.5Fe weight percent alloy is assumed to fill a small scale vertical rectangular enclosure model for this study. The Alternating Direction Implicit method and Successive Overrelaxation method are employed to solve these equations, which include the energy balance equation coupled with the mass and momentum equations. Both transient and steady state conditions under 1 g and low gravity (0.001 g) are investigated. The solutions for the two-dimensional isotherms and streamlines under 1 g conditions are graphically presented. The quantitative results show that the convection which occurs in the liquid metal pool is very small and is likely to have a negligible effect on the solute redistribution ahead of the solid-liquid interface.

Lott, R. L., Jr.↗

NASA NTRS1983

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

Phillips, T. N.↗

NASA NTRS1984

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Phillips, T. N.↗

NASA NTRS1994

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Whitfield, David L.↗

NASA NTRS1996

Numerical Investigation of Slag Behavior for RSRM

It is known that the flow field of the redesigned solid rocket motor (RSRM) is very complicated due to the complex characteristics of turbulent multi-phase flow, chemical reaction, particle combustion, evaporation, breakup and agglomeration etc. It requires multi-phase calculations, chemical reaction simulation, and particle combustion, evaporation, and breakup models to obtain a better understanding of thermophysics for the RSRM design using numerical methods. Also, the slag buildup due to the molten particles is another factor affecting the performance of the RSRM. To achieve this goal, the volume of fluid (VOF) method is used to capture the free surface motion so as to simulate the accumulation of the molten particles (slag) of the RSRM. A finite rate chemistry model is used to simulate the chemical reaction effects. For multi-phase calculations, the Hermsen combustion model is used for the aluminum particle combustion analysis and the Taylor Analogy Breakup (TAB) model is used for the particle breakup analysis. An interphase mas-exchange model introduced by Spalding is used for the evaporation calculation. The particle trajectories are calculated using a one-step implicit method for several groups of particle sizes by which the drag forces and heat fluxes are then coupled with the gas phase equations. The preliminary results predicted a reasonable physical simulation of the particle effects using a simple two dimensional solid rocket motor configuration. It shows that the AL/AL2O3 particle sizes are reduced due to the combustion, evaporation, and breakup. The flow field is disturbed by the particles. Mach number distributions in the nozzle are deformed due to the effect of particle concentrations away from the center line.

Liaw, P.↗

DOE OSTI2024

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

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