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At least 505 records · Page 28

Application of a fractional-step method to incompressible Navier-Stokes equation

A numerical method for computing three dimensional, time dependent incompressible flows is presented. The method is based on a fractional step, or time-splitting, scheme in conjunction with the approximate-factorization technique. The use of velocity boundary conditions for the intermediate velocity field leads to inconsistent numerical solutions. Appropriate boundary conditions for the intermediate velocity field are derived and tested. Numerical solutions for flow inside a driven cavity and over a backward-facing step are presented and compared with experimenal data and other numerical results.

Kim, J.↗

Application of a fractional-step method to incompressible Navier-Stokes equations

A numerical method for computing three dimensional, time dependent incompressible flows is presented. The method is based on a fractional step, or time-splitting, scheme in conjunction with the approximate-factorization technique. The use of velocity boundary conditions for the intermediate velocity field leads to inconsistent numerical solutions. Appropriate boundary conditions for the intermediate velocity field are derived and tested. Numerical solutions for flow inside a driven cavity and over a backward-facing step are presented and compared with experimental data and other numerical results.

Kim, J.↗

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗

Development of finite analytic method for unsteady three-dimensional Navier-Stokes equation

A finite analytic (FA) numerical method is described for the numerical study of three-dimensional fluid flow problems. The FA method incorporates a local linearization scheme and a classical analytic solution technique to formulate the algebraic representation of unsteady three-dimensional Navier Stokes Equations. The twenty-eight point FA formula thus obtained gives all positive coefficients and desired upwind shift. Cubic cavity flows are then solved by the FA method for Reynolds numbers of 100 and 400. A simple variant of SIMPLER algorithm is used to resolve the pressure-velocity coupling problem. The numerical solutions show that the presence of side walls reduce the strength of the primary vortex when compared with the two-dimensional square cavity flows.

Chen, H.-C.↗

Spectral methods on arbitrary grids

Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.

Carpenter, Mark H.↗

Combined Numerical/Analytical Perturbation Solutions of the Navier-Stokes Equations for Aerodynamic Ejector/Mixer Nozzle Flows

In spite of rapid advances in both scalar and parallel computational tools, the large number of variables involved in both design and inverse problems make the use of sophisticated fluid flow models impractical, With this restriction, it is concluded that an important family of methods for mathematical/computational development are reduced or approximate fluid flow models. In this study a combined perturbation/numerical modeling methodology is developed which provides a rigorously derived family of solutions. The mathematical model is computationally more efficient than classical boundary layer but provides important two-dimensional information not available using quasi-1-d approaches. An additional strength of the current methodology is its ability to locally predict static pressure fields in a manner analogous to more sophisticated parabolized Navier Stokes (PNS) formulations. To resolve singular behavior, the model utilizes classical analytical solution techniques. Hence, analytical methods have been combined with efficient numerical methods to yield an efficient hybrid fluid flow model. In particular, the main objective of this research has been to develop a system of analytical and numerical ejector/mixer nozzle models, which require minimal empirical input. A computer code, DREA Differential Reduced Ejector/mixer Analysis has been developed with the ability to run sufficiently fast so that it may be used either as a subroutine or called by an design optimization routine. Models are of direct use to the High Speed Civil Transport Program (a joint government/industry project seeking to develop an economically.viable U.S. commercial supersonic transport vehicle) and are currently being adopted by both NASA and industry. Experimental validation of these models is provided by comparison to results obtained from open literature and Limited Exclusive Right Distribution (LERD) sources, as well as dedicated experiments performed at Texas A&M. These experiments have been performed using a hydraulic/gas flow analog. Results of comparisons of DREA computations with experimental data, which include entrainment, thrust, and local profile information, are overall good. Computational time studies indicate that DREA provides considerably more information at a lower computational cost than contemporary ejector nozzle design models. Finally. physical limitations of the method, deviations from experimental data, potential improvements and alternative formulations are described. This report represents closure to the NASA Graduate Researchers Program. Versions of the DREA code and a user's guide may be obtained from the NASA Lewis Research Center.

DeChant, Lawrence Justin↗

Accurately simulating core-collapse self-interacting dark matter halos

The properties of satellite halos provide a promising probe for dark matter (DM) physics. Observations have motivated current efforts to explain surprisingly compact DM halos. If DM is not collisionless, but has strong self-interactions, halos can undergo gravothermal collapse, leading to higher densities in the central region of the halo. However, it is challenging to model this collapse phase from first principles. To improve on this, we sought to better understand the numerical challenges and convergence properties of self-interacting dark matter (SIDM) N-body simulations in the collapse phase. Especially, our aim was to better understand the evolution of satellite halos. To do so, we ran SIDM N-body simulations of a low-mass halo in isolation and within an external gravitational potential. The simulation set-up was motivated by the perturber of the stellar stream GD-1. We find that the halo evolution is very sensitive to energy conservation errors, and a SIDM kernel size that is too large can artificially speed up the collapse. Moreover, we demonstrate that the King model can describe the density profile at small radii for the late stages that we have simulated. Furthermore, for our most highly resolved simulation (N = 5 × 10 7 ) we have made the data public. It can serve as a benchmark. Overall, we find that the current numerical methods do not suffer from convergence problems in the late collapse phase and provide guidance on how to choose numerical parameters, for example that the energy conservation error is better kept well below 1%. This allows simulations to be run of halos that become concentrated enough to explain observations of GD-1-like stellar streams or strong gravitational lensing systems.

dark matter↗

Rendezvous Guidance Technology

The literature on rendezvous guidance technology is reviewed and a bibliography of about 160 documents is presented. The importance of the proper selection of the ascent trajectory and of the orbit for a manned space station or an orbiting launch complex is emphasized. The way the launch delay problem affects the selection of the ascent trajectory and the target orbit is discussed. A specific ascent trajectory and an orbit for a manned space station or an orbiting launch complex is recommended on the premise that launch delay problems will continue to outweigh most of the other orbit selection criteria. A new method for determining the velocity corrections required for mid-course guidance is proposed . The proposed methods consist of an "exact-numerical" solution of the relative equations of motion in the "Shell-coordinate system." The proposed "exact-numerical" method extends the applicability of the mid- course equations to a much greater range than that of the currently available linear methods .

Trajectory↗

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

Sridhar, B.↗

Aeroelastic stability of coupled flap-lag motion of hingeless helicopter blades at arbitrary advance ratios

Equations for large amplitude coupled flap-lag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade excited by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to radial flow are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of homogeneous periodic equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Computational efficiency of the two numerical methods is compared. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented.

Friedmann, P.↗

A numerical study of transient heat and mass transfer in crystal growth

A numerical analysis of transient heat and solute transport across a rectangular cavity is performed. Five nonlinear partial differential equations which govern the conservation of mass, momentum, energy and solute concentration related to crystal growth in solution, are simultaneously integrated by a numerical method based on the SIMPLE algorithm. Numerical results showed that the flow, temperature and solute fields are dependent on thermal and solutal Grashoff number, Prandtl number, Schmidt number and aspect ratio. The average Nusselt and Sherwood numbers evaluated at the center of the cavity decrease markedly when the solutal buoyancy force acts in the opposite direction to the thermal buoyancy force. When the solutal and thermal buoyancy forces act in the same direction, however, Sherwood number increases significantly and yet Nusselt number decreases. Overall effects of convection on the crystal growth are seen to be an enhancement of growth rate as expected but with highly nonuniform spatial growth variations.

Han, Samuel Bang-Moo↗

Improved boundary layer heat transfer calculations near a stagnation point

A thermal design of a solar receiver has been developed for the solutions of problems involving phase-change thermal energy storage and natural convection loss. Two dimensional axisymmetrical solidification and melting of materials contained between two concentric cylinders of finite length has been studied for thermal energy storage analysis. For calculation of free convection loss inside receiver cavity, two dimensional axisymmetrical, laminar, transient free convection including radiation effects has been studied using integral/finite difference method. Finite difference equations are derived for the above analysis subject to constant or variable material properties, initial conditions, and boundary conditions. The validity of the analyses has been substantiated by comparing results of the present general method with available analytic solutions or numerical results reported in the literature. Both explicit and implicit schemes are tested in phase change analysis with different number of nodes ranging from 4 to 18. The above numerical methods have been applied to the existing solar receiver analyzing computer code as additional subroutines. The results were computed for one of the proposed Brayton cycle solar receiver models running under the actual environmental conditions. Effect of thermal energy storage on the thermal behavior of the receiver has been estimated. Due to the thermal energy storage, about 65% reduction on working gas outlet temperature fluctuation has been obtained; however, maximum temperature of thermal energy storage containment has been increased about 18%. Also, effect of natural convection inside a receiver cavity on the receiver heat transfer has been analyzed. The finding indicated that thermal stratification occurs during the sun time resulting in higher receiver temperatures at the outlet section of the gas tube, and lower temperatures at the inlet section of the gas tube when compared with the results with no natural convection. Due to heat supply from the air during the shade time, minimum temperature has been increased, while maximum temperature has been reduced due to convection loss to air. Consequently, cyclic temperature fluctuation has been reduced 29% for working gas and 16% for thermal energy storage containment. On the other hand, despite the presence of the natural convection the time-averaged temperatures for receiver components were found to be similar for two cases with/without natural convection (maximum difference was 1.8%).

Ahn, Kyung Hwan↗

Intent Modeling and Intent Conflict Probability Calculation for Operations in Upper Class E Airspace

This work presents probabilistic intent models for two typical vehicles in ETM operational environment. Several methods, including analytical methods for approximated solutions and a numerical method for exact solution, are presented and applied to compute the intent conflict probability for ETM operations. A comparison of these methods will be conducted in the final paper. Furthermore, simulations will be performed to verify the probabilistic intent model and verify the results of intent conflict probability from different methods.

Operational intent↗

Error propagation in the numerical solutions of the differential equations of orbital mechanics

The relationship between the eigenvalues of the linearized differential equations of orbital mechanics and the stability characteristics of numerical methods is presented. It is shown that the Cowell, Encke, and Encke formulation with an independent variable related to the eccentric anomaly all have a real positive eigenvalue when linearized about the initial conditions. The real positive eigenvalue causes an amplification of the error of the solution when used in conjunction with a numerical integration method. In contrast an element formulation has zero eigenvalues and is numerically stable.

Bond, V. R.↗

Numerical investigation of complex, transitional, and chemically reacting flows

This document is divided into two parts. Part A, on turbulent transport of chemical species in compressible reacting flows, includes the following topics: mixing of chemical species in reacting flows; chemically reacting turbulent flows; turbulent mixing of chemical species in reacting flows, which includes large eddy mixing, turbulent mixing, and molecular mixing; multiple time scale turbulence equations; species conservation equations for reacting flows; and a finite volume numerical method. Part B, on unsteady transitional flows over forced oscillatory surfaces, discusses unsteady transitional flow equations with moving boundaries and the application of the finite volume numerical solution method.

Kim, S.-W.↗

Scientific study of data analysis

We present a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized and the accuracy and numerical instability are discussed. On the basis of this investigation, we claim that the two methods do resemble each other qualitatively.

Wu, S. T.↗