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A Finite-Difference Scheme for the Navier-Stokes Equations of One- Dimensional, Isentropic, Compressible Flow

Roger Zarnowski and David Hoff
SIAM Journal on Numerical Analysis
Vol. 28, No. 1 (Feb., 1991), pp. 78-112
Stable URL: http://www.jstor.org/stable/2157934
Page Count: 35
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A Finite-Difference Scheme for the Navier-Stokes Equations of One- Dimensional, Isentropic, Compressible Flow
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Abstract

Convergence is proved and error bounds are derived for a finite difference approximation to discontinuous solutions of the Navier-Stokes equations for one-dimensional isentropic compressible flow. This scheme can be implemented under mesh conditions essentially equivalent to the usual CFL condition. It is shown that, for initial data which is BV and piecewise smooth, the error is bounded by O(Δ x1/6) in a norm which dominates the sup-norm of the density, and is bounded by O(Δ x1/2) when the initial data is H1.

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