On Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing

✍ Scribed by Andrei I. Tolstykh; Michael V. Lipavskii

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 488 KB
• Volume: 140
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1998.5887

✦ Synopsis

The difference schemes for fluid dynamics type of equations based on third-and fifth-order Compact Upwind Differencing (CUD) are considered. To validate their properties following from a linear analysis, calculations were carried out using the inviscid and viscous Burgers' equation as well as the compressible Navier-Stokes equation written in the conservative form for curvilinear coordinates. In the latter case, transonic cascade flow was chosen as a representative example. The performance of the CUD methods was estimated by investigating mesh convergence of the solutions and comparing with the results of second-order schemes. It is demonstrated that the oscillation-free steep gradients solutions obtained without using smoothing techniques can provide considerable increase of accuracy even when exploiting coarse meshes.