A convergent finite-difference scheme for the Navier-Stokes equations of one-dimensional, nonisentropic, compressible flow

Journal Article · Sat Oct 01 04:00:00 EDT 1994 · SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0731067· OSTI ID:7149538

Zhao, J ^[1]; Hoff, D ^[2]

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1. Univ. of Michigan, Dearborn, MI (United States). Dept. of Mathematics
2. Indiana Univ., Bloomington, IN (United States). Dept. of Mathematics

Convergence is proved and error bounds are derived for a finite-difference approximation to discontinuous solutions of the Navier-Stokes equations for nonisentropic, compressible flow in one space dimension. The scheme is fully implicit and can be implemented under reasonable mesh conditions. It is shown that the approximations converge at the rate O([Delta]x[sup 1/2]) when the initial data is in H[sup 1], and O([Delta]x[sup a]) (a < 1/12) when the initial velocity and energy are in L[sup 2], and the initial density is piece wise H[sup 1]. The errors are measured in a norm that dominates the sup-norm of the error in the density, which in general is discontinuous. This choice is indicated by the known continuous-dependence theory and accounts for the low rate of convergence in the second case.

• OSTI ID: 7149538
• Journal Information: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States) Vol. 31:5; ISSN 0036-1429; ISSN SJNAAM
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer &amp; Fluid Flow
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics &amp; Computers
BOUNDARY CONDITIONS
CALCULATION METHODS
COMPRESSIBLE FLOW
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FLUID FLOW
ITERATIVE METHODS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS