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First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion ProblemsA time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.
Document ID
20140012708
Acquisition Source
Langley Research Center
Document Type
Technical Memorandum (TM)
Authors
Mazaheri, Alireza
(NASA Langley Research Center Hampton, VA, United States)
Nishikawa, Hiroaki
(National Inst. of Aerospace Hampton, VA, United States)
Date Acquired
September 29, 2014
Publication Date
March 1, 2014
Subject Category
Numerical Analysis
Report/Patent Number
NASA/TM-2014-218175
L-20378
NF1676L-18307
Funding Number(s)
WBS: WBS 747797.02.09.30.04
Distribution Limits
Public
Copyright
Public Use Permitted.
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