ISSN:
0271-2091
Keywords:
finite difference method (FDM)
;
computational fluid dynamics
;
transport equation
;
numerical stability
;
numerical oscillations
;
characteristic equation
;
LECUSSO scheme
;
QUICK scheme
;
LENS scheme
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
In order to obtain stable and accurate numerical solutions for the convection-dominated steady transport equations, we propose a criterion for constructing numerical schemes for the convection term that the roots of the characteristic equation of the resulting difference equation have poles.By imposing this criterion on the difference coefficients of the convection term, we construct two numerical schemes for the convection-dominated equations. One is based on polynomial differencing and the other on locally exact differencing.The former scheme coincides with the QUICK scheme when the mesh Reynolds number (Rm) is \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $\end{document}, which is the critical value for its stability, while it approaches the second-order upwind scheme as Rm goes to infinity. Hence the former scheme interpolates a stable scheme between the QUICK scheme at Rm = \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[{\textstyle{{\rm 8} \over {\rm 3}}}\] $\end{document} and the second-order upwind scheme at Rm = ∞. Numerical solutions with the present new schemes for the one-dimensional, linear, steady convection-diffusion equations showed good results.
Additional Material:
4 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650211103
