Editorial

Abstract

This special issue on the ‘Characteristic-Based Split (CBS)’ scheme was conceived from the experience of different people working in different areas of computational mechanics. The objective in the main is the presentation of the CBS scheme in its very general form to accommodate general engineering problems of interest to the engineering community. Thus, we have included papers on general fluid dynamics, shallow-water flows, solid dynamics, porous media and heat transfer. A total of eight papers have been included into this special issue. The first paper by Nithiarasu et al. describes the CBS scheme in detail with an explanation on the origin of the characteristic-based procedures and their extension to solve compressible and incompressible flows. This paper also describes the merger of the characteristic-based procedure with a fractional step algorithm to develop the CBS procedure. Several examples are also presented to demonstrate the robustness and accuracy of this unified approach to compressible and incompressible flows. Though only fluid dynamics examples are presented in the first paper, the suitability of the method to solve solid dynamic problems is demonstrated in the second paper by Rojek et al. This paper again demonstrates the novelty of the proposed approach. The presented idea immediately forms the basis for coupled fluid-solid problems using a single approach with different constitutive equations. The third paper is presented by Ortiz et al. which describe the CBS approach to shallow-water problems. Once again the versatility of the method is demonstrated for an entirely different kind of incompressible flow equations. The shallow-water equations presented in this paper resembles the inviscid compressible flows. Thus, it is obvious that the same methodology used to solve the compressible flows can be extended to the shallow-water equations. The next paper is a recent work on porous media problems using the CBS approach. The authors, Salomoni and Schrefler, have demonstrated the use of the CBS scheme to a complicated porous medium problem. Once again this proves that the application of the CBS scheme is not limited to fluid dynamics problems. The next three papers by Massarotti et al., Morandi Cecchi and Venturin and Kulkarni et al. are the applications of the CBS scheme to different engineering problems. In Massarotti et al., the method has been extensively used to steady and unsteady incompressible flows with heat transfer to make a general assessment of the method in its fully explicit and semi-implicit forms. This paper gives an in-depth comparison between the two variations. In Morandi Cecchi and Venturin, the method is applied to solve a practical shallow-water problem of the Venice Lagoon. The third paper in the application series by Kulkarni et al. deals with a practical application of under-fill simulation process in electronic packaging. All these three papers clearly demonstrate the flexibility of the CBS method for different applications of practical importance. This special issue is concluded by a paper on a comparative study between the CBS scheme and other recent methods. This last paper is presented by Codina et al. and compares the CBS method against the family of recent subgrid scale (SGS) methods. Finally, we would like to thank Prof. O. C. Zienkiewicz for supporting this special issue and writing a foreword. We are also grateful to Professor R. W. Lewis, editor of the International Journal for Numerical Methods in Engineering for permitting us to produce this special issue. We hope this special issue will be of great use to the readers to learn about the CBS scheme and its development over the last 10 years.