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Numerical simulation of conservation lawsA new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.
Document ID
19920016570
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Chang, Sin-Chung
(NASA Lewis Research Center Cleveland, OH, United States)
To, Wai-Ming
(Sverdrup Technology, Inc., Cleveland OH., United States)
Date Acquired
September 6, 2013
Publication Date
February 1, 1992
Publication Information
Publication: Computational Fluid Dynamics
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
92N25813
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
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