Explicit and semi-implicit CBS procedures for incompressible viscous flows

This paper presents a numerical comparison of two different numerical procedures based on the characteristic-based split (CBS) algorithm for the solution of incompressible flows. The first procedure is based on the original semi-implicit version of the CBS, introduced in the early days of the scheme development. The second was proposed more recently in order to have a fully explicit version of the scheme, and is based on the introduction of an artificial compressibility type of formulation. The interest in fully explicit schemes has increased because of the easy and efficient parallelization. The main differences between the two versions of the schemes are highlighted in this work, and a numerical comparison is presented on the basis of several benchmark solutions. Both steady and unsteady flows are considered. With the explicit version of the scheme a dual time stepping procedure is needed to recover unsteady solutions.