Origins and Further Development of the Jameson-Schmidt-Turkel Scheme

This paper is in response to an invitation to give a presentation on the origins and subsequent development of the Jameson-Schmidt-Turkel scheme. After a description of the historical background and initial development of the scheme, the paper discusses three main developments: first, the development of convergence acceleration methods, including residual averaging and multigrid; second, the extension to unstructured grids; and third, the reformulation of the Jameson-Schmidt-Turkel scheme as a total-variation-diminishing scheme and its relationship to symmetric total-variation-diminishing schemes. The paper concludes with a brief review of applications to unsteady and viscous flows.