Bram van Leer

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Bram van Leer
Born Netherlands East-Indies
Fields CFD
Fluid dynamics
Numerical Analysis
Institutions University of Michigan
Alma mater Leiden State University
Doctoral advisor Hendrik C. van de Hulst
Known for MUSCL scheme

Bram van Leer is Arthur B. Modine Emeritus Professor of aerospace engineering at the University of Michigan, in Ann Arbor.[1] He specializes in Computational fluid dynamics (CFD), fluid dynamics, and numerical analysis where he has made substantial contributions.

An astrophysicist by education, Van Leer made seminal contributions to CFD in his 5-part article series “Towards the Ultimate Conservative Difference Scheme”, where he extended Godunov’s finite-volume scheme to the second order (MUSCL), developed nonoscillatory interpolation using limiters, an approximate Riemann solver, and Discontinuous-Galerkin schemes for unsteady advection. Since joining the University of Michigan’s Aerospace Engineering Department (1986) he has worked on convergence acceleration by local preconditioning and multigrid relaxation for Euler and Navier-Stokes problems, unsteady adaptive grids, space-environment modeling, atmospheric flow modeling, extended hydrodynamics for rarefied flows, and Discontinuous Galerkin methods. He retired in 2012.

Throughout his career van Leer has crossed interdisciplinary boundaries to export state-of-the-art CFD technology. Starting from astrophysics, he first made an impact on weapons research, followed by aeronautics, then space-weather modeling, atmospheric modeling, surface-water modeling and automotive engine modeling, to name the most important fields.

Research work[edit]

Bram van Leer was a doctoral student in astrophysics at Leiden Observatory (1966-70) when he got interested in Computational Fluid Dynamics (CFD) for the sake of solving cosmic flow problems. His first major result in CFD[2] was the formulation of the upwind numerical flux function for a hyperbolic system of conservation laws:  F^\hbox{up} = \frac{1}{2} (F_j + F_{j+1} ) - |A|_{j+\frac{1}{2}} (u_{j+1} - u_j).

Here the matrix |A| appears for the first time, defined as the matrix that has the same eigenvectors as the flux Jacobian A, but the corresponding eigenvalues are the moduli of those of A. The subscript j+\frac{1}{2} indicates a representative or average value on the interval (x_j,x_{j+1}); it was no less than 10 years later before Philip L. Roe first presented his much used averaging formulas.

Next, Van Leer succeeded in circumventing Godunov's barrier theorem (i.e., a monotonicity preserving advection scheme cannot be better than first-order accurate) by limiting the second-order term in the Lax-Wendroff scheme as a function of the non-smoothness of the numerical solution itself. This is a nonlinear technique even for a linear equation. Having discovered this basic principle, he planned a series of three articles titled "Towards the ultimate conservative difference scheme", which advanced from scalar nonconservative but non-oscillatory (part I) via scalar conservative non-oscillatory (part II) to conservative non-oscillatory Euler (part III). The finite-difference schemes for the Euler Equations turned out to be unattractive because of their many terms; a switch to the finite-volume formulation completely cleared this up and led to Part IV (finite-vplume scalar) and, finally, Part V (finite-volume Lagrange and Euler) titled, "A second-order sequel to Godunov's method", which is his most cited (>4000 times) article.

The series contains several original techniques that have found their way into the CFD community. In Part II two limiters are presented, later called by Van Leer "double minmod" (after Osher's "minmod" limiter) and its smoothed version "harmonic"; the latter limiter is sometimes referred to in the literature as "Van Leer's limiter." Part IV, "A new approach to numerical convection," describes a group of 6 second- and third-order schemes that includes two Discontinuous Galerkin schemes with exact time-integration. Van Leer was not the only one to break Godunov's barrie using nonlinear limiting; similar techniques were developed independently around the same time by Boris [3] and by V.P. Kolgan, a Russian researcher unknown in the West. In 2011 Van Leer devoted an article to to Kolgan's contributions [4] and had Kolgan's 1972 TsADI report reprinted in translation in the Journal of Computational Physics.

After the publication of the series (1972-79) Van Leer spent two years at ICASE (NASA LaRC), where he was engaged by NASA engineers interested in his numerical expertise. This led to Van Leer's differentiable flux-vector splittng [5] and the development of the block-structured codes CFL2D and CFL3D [6][7] which still are heavily used. Other seminal papers from these years are the review of upwind methods with Harten and Lax,[8] the AMS workshop paper [9] detailing the differences and resemblances between upwind fluxes and Jameson's flux formula, and the conference paper with Mulder [10] on upwind relaxation methods; the latter includes the concept of Switched Evolution-Relaxation (SER) for automatically choosing the time-step in an implicit marching scheme, which was inspired by a seminar by Napolitano at ICASE in 1982.

Education and Training[edit]

  • 1963 - Candidate Astronomy, Leiden State University
  • 1966 - Doctorandus Astrophysics, Leiden State University
  • 1970 - Ph.D. Astrophysics, Leiden State University, 1970
  • 1970-72 - Miller Fellow Astrophysics, University of California Berkeley

Professional Experience[edit]

  • 2012 - Present - Professor Emeritus, University of Michigan
  • 1986-2012 - Professor, University of Michigan
  • 1982-86 - Research Leader, Delft University of Technology,
  • 1979-81 - Visiting Scientist, NASA Langley (ICASE)
  • 1978-82 - Research Leader, Leiden Observatory
  • 1970-72 - Miller Fellow Astrophysics, University of California Berkeley
  • 1966-77 - Research Associate, Leiden Observatory

Honors and Awards[edit]

  • 2010 - AIAA Fluid dynamics Award
  • 2007 - Arthur B. Modine Professor of Aerospace Engineering
  • 2005 - 2009 - Senior Fellow of the University of Michigan
  • 2005 - Dept. of Aerospace Engineering Service Award, Univ. of Michigan
  • 2003 - Computational Mechanics Award, Japan Society of Mechanical Engineers
  • 1996 - College of Engineering Research Excellence Award, Univ. of Michigan
  • 1995 - AIAA Fellow
  • 1992 - Public Service Group Achievement Award, NASA Langley
  • 1992 - Dept. of Aerospace Engineering Research Award, Univ. of Michigan
  • 1990 - Group Achievement Award, NASA Langley
  • 1990 - Honorary Doctorate, Free University Brussels
  • 1978 - C. J. Kok Prize, Leiden University

Recent Publications[edit]

  • B. van Leer and S. Nomura, "Discontinuous Galerkin for diffusion," AIAA Paper 2005-5108, 2005.
  • B. van Leer, "Upwind and high-resolution methods for compressible flow: from donor cell to residual-distribution schemes," Communications in Computational Physics, Vol.1, pp. 192-205, 2006.
  • B. van Leer, M. Lo and M. van Raalte, "A Discontinuous Galerkin Method for diffusion based on recovery," AIAA paper 2007-4083, 2007.
  • M. van Raalte and B. van Leer, "Bilinear forms for the recovery-based discontinuous Galerkin method for diffusion," Communications in Computational Physics Vol. 5, pp. 683-693, 2009.
  • B. van Leer and M. Lo, "Unification of Discontinuous Galerkin methods for advection and diffusion," AIAA paper 2009-0400, 2009.
  • M. Lo and B. van Leer, "Analysis and implementation of the Recovery-based Discontinuous Galerkin method for diffusion," AIAA Paper 2009-3786, 2009.
  • P. A. Ullrich, C. Jablonowski and B. van Leer (2010): "Riemann-solver-based high-order finite-volume models for the shallow-water equations on the sphere", J. Comput. Phys., Vol. 229, 6104-6134

Personal Interests[edit]

Van Leer is also an accomplished musician, playing the piano at the age of 5 and composing at 7. His musical education includes two years at the Royal Conservatory for Music of The Hague, NL. As a pianist he was featured in the Winter '96 issue of Michigan Engineering (Engineering and the Arts); as a carillonist he has played the carillon of the Central Campus Burton Tower on many football Saturdays.

He was the world's first and only cj (carillon-jockey), based on the North Campus Lurie Tower. In 1993 he gave a full-hour recital on the carillon of the City Hall in Leiden, the town where he studied for many years. Van Leer prefers to improvise in the Dutch carillon-playing style; one of his improvisations is included on a 1998 CD featuring both UM carillons. His carillon composition "Lament" was published in the UM School of Music's carillon music series on the occasion of the Annual Congress of the Guild of Carilloneurs in North America, Ann Arbor, June 2002. A flute composition by Van Leer was performed twice in 1997 by University of Michigan Professor Leone Buyse.

See also[edit]


  1. ^ "van Leer at University of Michigan". Retrieved 2009-04-04. 
  2. ^ van Leer, B. (1970). A Choice of Difference Schemes for Ideal Compressible Flow (Ph.D.). Sterrewacht, Leiden, The Netherlands. 
  3. ^ Boris, Jay P.; Book, David L. (1973), "Flux-corrected transport. I. SHASTA, A fluid transport algorithm that works", Journal of computational physics 11.1: 38–69, Bibcode:1973JCoPh..11...38B, doi:10.1016/0021-9991(73)90147-2 
  4. ^ van Leer, B. (2011), "A historical oversight: Vladimir P. Kolgan and his high-resolution scheme", Journal of Computational Physics, 230.7: 2378-2383, Bibcode:2011JCoPh.230.2378V, doi:10.1016/ 
  5. ^ van leer, B. (1982), "Flux-vector Splitting for the Euler Equations", Lecture Notes in Physics, International Conference on Numerical Methods in Fluid dynamics (Springer, Berlin) 170: 507-512 
  6. ^ Anderson, W.K.; Thomas, J.L.; van Leer, B. (1985), "A comparison of finite-volume flux-vector splittings for the Euler equations", AIAA Paper 
  7. ^ Thomas, J.L.; Walters, R.W.; van Leer, B.; Anderson, W.K. (1985), "Implicit flux-split schemes for the Euler-equations", AIAA Paper 85: 1680 
  8. ^ Harten, A.; Lax, P.D.; van Leer, B. (1983), "Upstream Differencing and Godunov-type Schemes for Hyperbolic Conservation Laws", SIAM Rev. 25: 35-61 
  9. ^ Engquist, B.; Osher, S.; Somerville, R. C. J. (1985), "Upwind-Difference Methods for Aerodynamic Problems Governed by the Euler Equations, Large-Scale Computations in Fluid Mechanics, eds.", Lectures in Applied Mathematics (AMS, Providence) 22: 327-336 
  10. ^ Mulder, W.A.; van Leer, B. (1985), "Experiments with Implicit Upwind Methods for the Euler Equations", J. Comp. Phys. 59: 232-246, Bibcode:1985JCoPh..59..232M, doi:10.1016/0021-9991(85)90144-5 

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