Shock capturing viscosities for the general fluid mechanics algorithm

• Published in: International journal for numerical methods in fluids Vol. 28; no. 9; pp. 1325 - 1353
• Main Authors: Nithiarasu, P., Zienkiewicz, O. C., Sai, B. V. K. Satya, Morgan, K., Codina, R., Vázquez, M.
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 15.12.1998; Wiley
• Subjects: Algorithms; artificial viscosity; Compressible flow; Compressible flows; shock and detonation phenomena; Computational methods in fluid dynamics; Exact sciences and technology; Finite element method; finite elements; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hypersonic flow; Matrix algebra; Physics; Pressure effects; Shock-wave interactions and shock effects; Shock-wave interactions and shockeffects; Supersonic flow; Viscosity; Viscous flow; Supersonic flow; Finite element method; Compressible fluid; Shock waves; Computational fluid dynamics; Non viscous fluid; Digital simulation; Pressure distribution; Airfoils; Compression corner; Viscous fluids; Mesh generation
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/(SICI)1097-0363(19981215)28:9<1325::AID-FLD765>3.0.CO;2-1

The performance of different shock capturing viscosities has been examined using our general fluid mechanics algorithm. Four different schemes have been tested, both for viscous and inviscid compressible flow problems. Results show that the methods based on the second gradient of pressure give better performance in all situations. For instance, the method constructed from the nodal pressure values and consistent and lumped mass matrices is an excellent choice for inviscid problems. The method based on L2 projection is better than any other method in viscous flow computations. The residual based anisotropic method gives excellent performance in the supersonic range and gives better results in the hypersonic regime if a small amount of residual smoothing is used. © 1998 John Wiley & Sons, Ltd.