A Development of Two-Dimensional Hydrodynamics

Bryce DeWitt

by Bryce S. DeWitt

Editor�s note, added July 3, 2007.

The story behind this contribution has a charming feeling of serendipity. Here are the details.

I received an inquiry about our web site from Alex Wellerstein, a history-of-science graduate student at Harvard. One of his projects was to gather all the data he could about Bryce Dewitt who, it turns out, was a very early Lab employee. Mr. Wellerstein and his thesis advisor were trying to evaluate how Bryce�s early work in hydrodynamics influenced his later research in quantum gravity. Up to this point, there was nothing in our web site about Bryce or his early work in hydrodynamics.

Hydrodynamics, it should go without saying, is fundamental to a large portion of the Laboratory�s computer modeling, so this bit of news was very interesting.

Mr. Wellerstein sent me copies of some of the articles he had collected. Included in this material was copy of an absolutely wonderful talk DeWitt gave at a dinner honoring Jim Wilson, the astrophysicist who also was then (and is still) at the Lab.

It so happens that I casually knew both Bryce, who started at the Lab in November, 1952, and Jim Wilson, who is still at the Lab. The entire staff then was about two hundred people so, naturally, everybody knew everybody, more or less. I started there in April, 1953 and Bryce left shortly after I arrived. At that time, I knew only about his interests in quantum physics.

With some extra checking, I now believe it is correct to say that Bryce DeWitt�s development of a two-dimensional model of computational hydrodynamics [1] is the first such, at least at the Lab. This work was completed essentially before I joined the Lab, which may explain why I was not aware of it. The same is also true for a specialized version of two-dimensional hydrodynamics. Jim Wilson alludes to this work in his short memoir included below. At least two independent attempts to produce the two-dimensional general equations of motion also failed and had to await bigger and faster computers and better differencing schemes. Today, the number of such programs is quite large, with most being tuned to run in a specific range of the dynamical variables.

The step to a system of difference equations turned out to be more difficult, and it was several years before a system of stable and robust equations were produced. (The current successful version starts with the work of many persons, especially that of Bill Schulz, and has been around since 1956 or 1957.) In any event, Bryce had left the Lab before this happened

Bryce�s talk describes his development of the two-dimensional Lagrangian representation of hydrodynamics. Jim Wilson�s research in stellar atmospheres depends heavily of an accurate treatment of fluid motion. Hence, Bryce�s equations were important to developing computer models of things like nuclear device designs, while Wilson�s stellar structures used approximately the same equations but with different boundary conditions. All sorts of one-dimensional approximations were used while we worked on the derivation of suitable two and even three dimensional models, and more importantly, while we waited for the arrival of bigger and faster computers.

The reader should not be surprised to learn that the early computers were neither big nor fast enough to be able to carry out the massive calculations needed for multi-dimensional modeling, at least in times sufficiently short to accommodate the attention spans of the first workers in this new science�computational physics.

[1] Bryce DeWitt's work in Two Dimensional Hydrodynamics is summarized in this paper dated December 10, 1953:
      A Numerical Method for Two-Dimensional Lagrangian Hydrodynamics

These are the remarks by Bryce DeWitt presented at the festschrift in honor of James R. Wilson:
      The Early Days of Lagrangian Hydrodynamics at Lawrence Livermore Laboratory

These are the contents pages of Proceedings of the October, 1982 symposium: in honor of James R. Wilson:
      Numerical Astrophysics - Proceedings of a symposium in honor of James R. Wilson

A Memoir of James R. Wilson