- published: 08 Mar 2014
- views: 132906
A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank. In much of the world, including most Commonwealth nations (such as the United Kingdom), German-speaking and northern Europe, professor is reserved only for the most senior academics at a university, typically a department chair, or an awarded chair specifically bestowed recognizing an individual at a university. A Professor is a highly accomplished and recognized academic, and the title is awarded only after decades of scholarly work. In the United States and Canada the title of professor is granted to all scholars with Doctorate degrees (typically Ph.D.s) who teach in two- and four-year colleges and universities, and is used in the titles Assistant Professor and Associate Professor, which are not considered Professor-level positions elsewhere, as well as for Full Professors.
Bram van Leer is the Arthur B. Modine Professor of aerospace engineering at the University of Michigan, in Ann Arbor. He specialises in Computational fluid dynamics (CFD), fluid dynamics, and numerical analysis where he has made substantial contributions.
Professor van Leer developed MUSCL scheme, which stands for Monotone Upstream-centered Schemes for Conservation Laws, and the term was introduced by him in a seminal paper (van Leer, 1979). In this paper he constructed the first high-order, total variation diminishing (TVD) scheme where he obtained second order spatial and temporal accuracy. It is a finite volume method that provides high accuracy numerical solutions to partial differential equations which can involve solutions that exhibit shocks, discontinuities, or steep gradients. In 1982 he published another important paper that introduced a computationally efficient alternative, based on flux-vector splitting, to the exact Riemann solver in Godunov algorithm (van Leer, 1982).
The idea is to replace the piecewise constant approximation of Godunov's scheme by reconstructed states, derived from cell-averaged states obtained from the previous time-step. For each cell, slope limited, reconstructed left and right states are obtained and used to calculate fluxes at the cell boundaries (edges). These fluxes are, in turn, used as input to the (approximate) Riemann solver. The Riemann solver solutions are averaged and used to advance the solution in time.