Comparative criteria for finite-difference formulations for problems of fluid flow

✍ Scribed by Akshai K. Runchal

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 624 KB
• Volume: 11
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620111104

✦ Synopsis

Abstract

This paper concerns a technique for providing quantitative and qualitative answers to the questions related to accuracy and stability of finite‐difference schemes. It is applicable to both the unsteady and the steady flows. The application of the technique provides comparative information about the amplitudes and the speeds of propagation of the numerical and analytic solutions. The difference between the two solutions is characterized in terms of a ‘false’ propagation speed and ‘false’ diffusion parameters for the numerical schemes.

The technique is applied to a number of commonly used finite‐difference schemes and it is concluded that the use of central differences for the convective terms and/or explicit formulations tends to increase the amplitudes and wave speeds. The opposite effects on the amplitudes and wave speeds are produced by upwind or ‘donor’ cell differences and/or implicit formulations.