Bram van Leer
Encyclopedia
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.
, 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 equation
s 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.
player. In 1993 gave a full-hour recital on the carillon of the City Hall in Leiden, the town where he studied for many years.
Aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, in Ann Arbor. He specialises in Computational fluid dynamics
Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with...
(CFD), fluid dynamics, and numerical analysis where he has made substantial contributions.
Research work
Professor van Leer developed MUSCL schemeMUSCL scheme
In the study of partial differential equations, the MUSCL scheme is a finite volume method that can provide highly accurate numerical solutions for a given system, even in cases where the solutions exhibit shocks, discontinuities, or large gradients...
, 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
Total variation diminishing
In numerical methods, total variation diminishing is a property of certain discretization schemes used to solve hyperbolic partial differential equations...
(TVD) scheme where he obtained second order spatial and temporal accuracy. It is a finite volume method
Finite volume method
The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations [LeVeque, 2002; Toro, 1999]....
that provides high accuracy numerical solutions to partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s 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
Riemann solver
A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in computational fluid dynamics and computational magnetohydrodynamics.-Exact solvers:...
in Godunov algorithm
Godunov's scheme
In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations...
(van Leer, 1982).
The idea is to replace the piecewise constant approximation of Godunov's scheme
Godunov's scheme
In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by S. K. Godunov in 1959, for solving partial differential equations...
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.
Education
- Ph.D. 1970 Leiden State UniversityLeiden UniversityLeiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...
- 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 LangleyLangley Research CenterLangley Research Center is the oldest of NASA's field centers, located in Hampton, Virginia, United States. It directly borders Poquoson, Virginia and Langley Air Force Base...
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 University 1978)
Interests
Bram van Leer is an accomplished pianist and carillonCarillon
A carillon is a musical instrument that is typically housed in a free-standing bell tower, or the belfry of a church or other municipal building. The instrument consists of at least 23 cast bronze, cup-shaped bells, which are played serially to play a melody, or sounded together to play a chord...
player. In 1993 gave a full-hour recital on the carillon of the City Hall in Leiden, the town where he studied for many years.
See also
- Finite volume methodFinite volume methodThe finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations [LeVeque, 2002; Toro, 1999]....
- Flux limiterFlux limiterFlux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations...
- Godunov's theoremGodunov's theoremIn numerical analysis and computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high resolution schemes for the numerical solution of partial differential equations.The theorem states...
- Sergei K. GodunovSergei K. GodunovSergei Konstantinovich Godunov is professor at the Sobolev Institute of Mathematics of the Russian Academy of Sciences in Novosibirsk, Russia....