HISTORY OF CFD PART II - American Institute of ... Leer...History of CFD (concl.) Part II: 1970...
Transcript of HISTORY OF CFD PART II - American Institute of ... Leer...History of CFD (concl.) Part II: 1970...
HISTORY OF CFD
PART II
Bram van Leer
Department of Aerospace EngineeringUniversity of Michigan
Chicago29 June 2010
History of CFD
Pre-history: < WW II
Courant, Friedrichs & Lewy
Part I: WW II – 1970
Von Neumann
Lax
Godunov
History of CFD (concl.)
Part II: 1970 -1985
In which high-resolution methods appear and find their way into aerospace engineering
April 1967
I visit the NLR (Dutch Nat’l Aerospace Lab)
and learn about
Comm. Pure Appl. Math.
with articles by Lax and others
AIAA Journal
leading me to Godunov’s work
Godunov’s Barrier Theorem
If an advection scheme is monotonicity-preserving, it can not be better than
first-order accurate
Breaking the Barrier
Godunov’s proof silently assumes the use of a linear advection scheme for the linear advection equation
If a nonlinear scheme is used, the barrier vanishes
Vladimir Pavlovich Kolgan
Born 16 October 1940
Educated at MFTIEngineer 1964
Ph. D. 1972
Employed at TsAGISenior Research Scientist
Died 28 July 1978
Courtesy Dr. V. Yumachev (TsAGI)
Kolgan’s 1972 Report (1)
Title
Numerical schemes for discontinuous
problems of gas dynamics based on
minimization of the solution gradient
Minmod limiter built-in
no choice of limiter
Kolgan’s 1972 Report (2)
Kolgan’s minmod limiter
Osher’s minmod limiter
otherwise
if
lim
u
uuu
u
otherwise
ifsgn,min
lim
0
0uuuuu
u
Kolgan’s 1972 Report (3)
Time marching by “Forward Euler”
Linearly unstable
Stabilized by limiter for CFL ≤ 1/2
Osher & Chakravarthy (1984)
With full minmod stable for CFL ≤ ⅔
1979
Publication of “Towards the
Ultimate Conservative Difference
Scheme I-V” completed
Publication of 4 papers on FCT by
Boris, Book, Hain, and Zalesak
completed
Transition toAerospace Engineering (1)
Godunov-type high-resolution methods found
their way into Aerospace Engineering mostly via
ICASE at NASA Langley Research Center
Some key players:
Ami Harten Bram van Leer Stan Osher Phil Roe
Transition to Aerospace Engineering (2)
Ami Harten (Tel-Aviv) spent 1978-79 and other periods at ICASE, but preferred to visit California (NASA Ames, UCLA)
Van Leer (Leiden), introduced by Harten, spent 1979-81 and many summers at ICASE
Stan Osher (UCLA) had consulted at NASA Ames as of 1978 and later began to visit ICASE
Phil Roe (RAE) burst onto the scene in 1980 and became a regular summer visitor at ICASE
Transition to Aerospace Engineering (3)
In 1983 Jim Thomas and Kyle Anderson
(NASA Langley), later joined by Bob
Walters (VA Tech), teamed up with Van
Leer to develop a Godunov-type higher-
order code for aeronautical problems:
the birth of CFL3D
Osher teamed up with Sukumar
Chakravarthy (Rockwell) to develop a
similar code
Transition to Aerospace Engineering (4)
At the 1985 AIAA CFD Conference in Cincinnati both
teams reported mature Euler results, and extensions to
Navier-Stokes were completed in the same year
In December 1985 the Langley team participated in a
GAMM Navier-Stokes workshop in Nice, France
At the closure of 1985 the period of technology
transition was over, and so was Part II of the
History of CFD