APPLICATION OF THE SPACE-TIME CONSERVATION ELEMENT AND SOLUTION ELEMENT METHOD TO ONE-DIMENSIONAL... NASA/TM-1999-209068... JUL. 9, 1999 PDF Download
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Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781724024190
Category : Science
Languages : en
Pages : 42
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Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference schemes with similar accuracy, the CE/SE solutions display much lower numerical dissipation and dispersion errors. Wang, Xiao-Yen and Chow, Chuen-Yen and Chang, Sin-Chung Glenn Research Center NASA/TM-1999-209068, NAS 1.15:209068, E-11624
Author: United States. National Aeronautics and Space Administration
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Languages : en
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Languages : en
Pages : 30
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Author: National Aeronautics and Space Adm Nasa
Publisher:
ISBN: 9781731326898
Category :
Languages : en
Pages : 126
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A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly. Chang, Sin-Chung and Wang, Xiao-Yen and Chow, Chuen-Yen Glenn Research Center SPACE-TIME FUNCTIONS; CONSERVATION; SHOCK WAVES; RELATIVITY; HIGH RESOLUTION; CONSERVATION LAWS; BOUNDARY LAYERS; FLUX DENSITY...
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Languages : en
Pages : 40
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Languages : en
Pages : 130
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Author: Chih-Yung Wen
Publisher: Springer Nature
ISBN: 9819908760
Category : Computers
Languages : en
Pages : 144
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This open access book introduces the fundamentals of the space–time conservation element and solution element (CESE) method, which is a novel numerical approach for solving equations of physical conservation laws. It highlights the recent progress to establish various improved CESE schemes and its engineering applications. With attractive accuracy, efficiency, and robustness, the CESE method is particularly suitable for solving time-dependent nonlinear hyperbolic systems involving dynamical evolutions of waves and discontinuities. Therefore, it has been applied to a wide spectrum of problems, e.g., aerodynamics, aeroacoustics, magnetohydrodynamics, multi-material flows, and detonations. This book contains algorithm analysis, numerical examples, as well as demonstration codes. This book is intended for graduate students and researchers who are interested in the fields such as computational fluid dynamics (CFD), mechanical engineering, and numerical computation.
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722830915
Category :
Languages : en
Pages : 60
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Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently. Wang, Xiao-Yen and Chow, Chuen-Yen and Chang, Sin-Chung Glenn Research Center...
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