3 - The characteristic-based split (CBS) algorithm. A general procedure for compressible and incompressible flow

• Published in: The Finite Element Method Set pp. 79 - 109
• Main Authors: O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu
• Format: Book Chapter
• Language: English
• Published: Elsevier Ltd 2005
• Edition: Sixth Edition
• ISBN: 9780750664318; 0750664312
• DOI: 10.1016/B978-075066431-8.50209-5

This chapter discusses the General Characteristic-Based Split (CBS) algorithm for the equations of fluid dynamics in their conservation form. The algorithm introduced in this chapter is currently the most general one available for fluids, as it can be directly applied to almost all physical situations. This chapter extends the split to solve the fluid dynamics equations of both compressible and incompressible forms using the characteristic-Galerkin procedure. The algorithm in its full form was first introduced in 1995 and followed several years of preliminary research. The algorithm proves to be at least as good as other procedures developed in applications ranging from low Mach number viscous or inviscid flow to the solution of hypersonic flows. Comparison between the single- and two-step algorithms in the last section shows that the latter scheme is valid for all ranges of flow. In problems of very slow viscous flow, the treatment can be almost identical to that of incompressible elastic solids.