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

My Ph. D. Thesis

My Advisors

Henk van de Hulst Jan Hendrik Oort

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

Colliding Cosmic Clouds

expected solution solution by Lax-Friedrichs

Shocks on the Sun

Lax-Wendroff

Godunov

Godunov’s Barrier Theorem

If an advection scheme is monotonicity-preserving, it can not be better than

first-order accurate

Godunov’s Proof

And Yet…

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

My First Limiter

Double Minmod

as used in the MUSCL code

The Only One

Jay Boris Vladimir KolganBram van Leer

Not …

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

Shock Tube Problem

• Kolgan

o Godunov

- Exact

Note “staircasing”

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

ICASE Summer Program 1984

CFD Group

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

THANKS

To Marcus Lo (U. of Michigan)

for “Photoshoping”

To Konstantin Kabin (U. of Alberta)

for translating Kolgan’s paper