Bram van Leer

Bram van Leer is professor of aerospace engineering at the University of Michigan, USA. He specialises in computational fluid dynamics CFD, fluid dynamics and numerical analysis where he has made substantial contributions.

Professor van Leer developed MUSCL, 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 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 large gradients. Then in 1982 he published another very important paper that introduced a computationally effcient alternative to the 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.

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Education

• Ph. D. 1970 Leiden State University
• Doctorandus 1966 Leiden State University
• Candidate 1963 Leiden State University, The Netherlands

Honors and Awards

• College of Engineering Research Award (University of Michigan 1996)
• Elected AIAA Fellow (1995)
• NASA Langley Group Achievement Award (1990, 1992)
• Department of Aerospace Engineering Research Award (University of Michigan 1992)
• Honorary Doctorate (Vrije Universiteit Brussels 1990)
• C.J. Kok Prize (Leiden State University 1978)

Interests

Bram van Leer is an accomplished carillon player and in 1993 gave a full-hour recital on the carillon of the City Hall in Leiden, the town where he studied for many years.

References

• Van Leer, B. (1979), Towards the Ultimate Conservative Difference Scheme, V. A Second Order Sequel to Godunov's Method, J. Com. Phys.., 32, 101–136.
• Van Leer,B. (1982), Flux-vector splitting for the Euler equations, in Lecture Notes in Physics, 170, Springer, Berlin, pp. 507-512.

See also

• Finite volume method
• Flux limiter
• Godunov's theorem
• MUSCL scheme
• Sergei K. Godunov