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  • 1
    Publication Date: 1999-11-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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  • 2
    Publication Date: 2000-11-01
    Print ISSN: 0021-9991
    Electronic ISSN: 1090-2716
    Topics: Computer Science , Physics
    Published by Elsevier
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  • 3
    Publication Date: 2011-08-23
    Description: In the space-time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh value of the physical dependent variables but also, in contrast to it typical numerical method, the Mesh values of the spatial derivatives of the physical variables The use of the extra marching variables results from the need to construct the two-level explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper using the 1D(sub (alpha)-mu) scheme as an example, the effect of this added complication on consistency, accuracy and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the alpha-mu scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the alpha-mu. Leapfrog, and DuFort-Frankel schemes are further explored. In addition, the redundance of the Leapfrog, DUFort-Frankel, and Lax scheme and the remedy for this redundance are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burger equation.
    Keywords: Numerical Analysis
    Type: Journal of Computational Physics (ISSN 0021-9991); Volume 165; 189-215
    Format: text
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  • 4
    Publication Date: 2013-08-29
    Description: Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.
    Keywords: Theoretical Mathematics
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  • 5
    Publication Date: 2018-06-05
    Description: The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.
    Keywords: Numerical Analysis
    Type: Research and Technology 1998; NASA/TM-1999-208815
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  • 6
    Publication Date: 2019-06-28
    Description: The existing 2-D alpha-mu scheme and alpha-epsilon scheme based on the method of space-time conservation element and solution element, which were constructed for solving the linear 2-D unsteady advection-diffusion equation and unsteady advection equation, respectively, are tested. Also, the alpha-epsilon scheme is modified to become the V-E scheme for solving the nonlinear 2-D inviscid Burgers equation. Numerical solutions of six test problems are presented in comparison with their exact solutions or numerical solutions obtained by traditional finite-difference or finite-element methods. It is demonstrated that the 2-D alpha-mu, alpha-epsilon, and nu-epsilon schemes can be used to obtain numerical results which are more accurate than those based on some of the traditional methods but without using any artificial tuning in the computation. Similar to the previous 1-D test problems, the high accuracy and simplicity features of the space-time conservation element and solution element method have been revealed again in the present 2-D test results.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TM-106946 , E-9681 , NAS 1.15:106946
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  • 7
    Publication Date: 2019-06-28
    Description: An Euler solver based on the method of space-time conservation element and solution element is in this paper to simulate shock-tube flows involving shock waves, contact discontinuities, expansion waves and their intersections. Seven test problems are considered to examine the capability of this method. The numerical results, when compared with exact solutions and/or numerical solutions by other methods, indicate that the present method can accurately resolve strong shock and contact discontinuities without using any ad hoc techniques which are used only at the neighborhood of a discontinuity.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: NASA-TM-106806 , E-9288 , NAS 1.15:106806
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  • 8
    Publication Date: 2019-07-27
    Description: The crew exploration vehicle (CEV) service module (SM) main engine plume heating is analyzed using multiple numerical tools. The chemical equilibrium compositions and applications (CEA) code is used to compute the flow field inside the engine nozzle. The plume expansion into ambient atmosphere is simulated using an axisymmetric space-time conservation element and solution element (CE/SE) Euler code, a computational fluid dynamics (CFD) software. The thermal analysis including both convection and radiation heat transfers from the hot gas inside the engine nozzle and gas radiation from the plume is performed using Thermal Desktop. Three SM configurations, Lockheed Martin (LM) designed 604, 605, and 606 configurations, are considered. Design of multilayer insulation (MLI) for the stowed solar arrays, which is subject to plume heating from the main engine, among the passive thermal control system (PTCS), are proposed and validated.
    Keywords: Fluid Mechanics and Thermodynamics
    Type: NASA/TM-2007-215049 , TFAWS 07-1012 , E-16260 , Thermal and Fluids Analysis Workshop (TFAWS) 2007; 10-14 Seo, 2007; Warrensville Heights, OH; United States
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  • 9
    Publication Date: 2019-07-13
    Description: A nontraditional numerical method for solving conservation laws is being developed. The new method is designed from a physicist's perspective, i.e., its development is based more on physics than numerics. Even though it uses only the simplest approximation techniques, a 2D time-marching Euler solver developed recently using the new method is capable of generating nearly perfect solutions for a 2D shock reflection problem used by Helen Yee and others. Moreover, a recent application of this solver to computational aeroacoustics (CAA) problems reveals that: (1) accuracy of its results is comparable to that of a 6th order compact difference scheme even though nominally the current solver is only of 2nd-order accuracy; (2) generally, the non-reflecting boundary condition can be implemented in a simple way without involving characteristic variables; and (3) most importantly, the current solver is capable of handling both continuous and discontinuous flows very well and thus provides a unique numerical tool for solving those flow problems where the interactions between sound waves and shocks are important, such as the noise field around a supersonic over- or under-expansion jet.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-106915 , E-9623 , NAS 1.15:106915 , AIAA PAPER 95-1754 , Annual Maryland Conference on The Evolution of X-ray Binaries; Jun 19, 1995 - Jun 22, 1995; San Diego, CA; United States
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  • 10
    Publication Date: 2019-07-13
    Description: This paper presents results from computational fluid dynamic (CFD) simulations of a three-stream plug nozzle. Time-accurate, Euler, quasi-1D and 2D-axisymmetric simulations were performed as part of an effort to provide a CFD-based approach to modeling nozzle dynamics. The CFD code used for the simulations is based on the space-time Conservation Element and Solution Element (CESE) method. Steady-state results were validated using the Wind-US code and a code utilizing the MacCormack method while the unsteady results were partially validated via an aeroacoustic benchmark problem. The CESE steady-state flow field solutions showed excellent agreement with solutions derived from the other methods and codes while preliminary unsteady results for the three-stream plug nozzle are also shown. Additionally, a study was performed to explore the sensitivity of gross thrust computations to the control surface definition. The results showed that most of the sensitivity while computing the gross thrust is attributed to the control surface stencil resolution and choice of stencil end points and not to the control surface definition itself.Finally, comparisons between the quasi-1D and 2D-axisymetric solutions were performed in order to gain insight on whether a quasi-1D solution can capture the steady and unsteady nozzle phenomena without the cost of a 2D-axisymmetric simulation. Initial results show that while the quasi-1D solutions are similar to the 2D-axisymmetric solutions, the inability of the quasi-1D simulations to predict two dimensional phenomena limits its accuracy.
    Keywords: Aerodynamics
    Type: GRC-E-DAA-TN16144 , AIAA Joint Propulsion Conference; Jul 28, 2014 - Jul 30, 2014; Cleveland, OH; United States
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