On the Origins of Lagrangian Hydrodynamic Methods

Abstract

The intent of this paper is to discuss the history and origins of Lagrangian hydrodynamic methods for simulating shock driven flows. The majority of the pioneering research occurred within the Manhattan Project. A range of Lagrangian hydrodynamic schemes were created between 1943 and 1948 by John von Neumann, Rudolf Peierls, Tony Skyrme, and Robert Richtmyer. These schemes varied significantly from each other; however, they all used a staggered-grid and finite difference approximations of the derivatives in the governing equations, where the first scheme was by von Neumann. These ground-breaking schemes were principally published in Los Alamos laboratory reports that were eventually declassified many decades after authorship, which motivates us to document the work and describe the accompanying history in a paper that is accessible to the broader scientific community. Furthermore, we seek to correct historical omissions on the pivotal contributions made by Peierls and Skyrme to creating robust Lagrangian hydrodynamic methods for simulating shock driven flows. Understanding the history of Lagrangian hydrodynamic methods can help explain the origins of many modern schemes and may inspire the pursuit of new schemes.

The Los Alamos Computing Facility During the Manhattan Project

“…See the companion ANS article regarding the first hydrodynamics code. 15 Programming the PCAM started with dividing the equations into IBM operations: add these two quantities, divide these two, sum, etc. 9 This type of programming is shown in detail in LA-1057 (Ref.…”

Artificial Viscosity -- Then and Now

“…In this paper we have attempted to summarize the historical development of modeling shocks on the computer, celebrating its early pioneers, giving a modern perspective of its theoretical essence, as well as offering insights for future improvements. The underlying idea of shock capturing, first elucidated by Rudolf Peierls [52] preceded the advent of the first electronic computer [17,50] and is based on the fundamental results of Rankine [38]. The importance of dissipation in regularizing the theoretical shock structure is attributed to Becker in both [57,72].…”

“…The earliest computer simulations of shocks by Los Alamos staff showed unphysical oscillations (wiggles) behind the shock front. The first remedy was based on shock tracking, a cumbersome process that required continuous human interaction with the computer [50]. Artificial dissipation as it was first termed represented an effective automatic solution to eliminate the wiggles.…”

Trinity by the Numbers: The Computing Effort that Made Trinity Possible

“…For an in-depth discussion of wartime hydrodynamics at Los Alamos, see Morgan and Archer's article on Lagrangian hydrodynamic methods in this issue. 4,35 A large volume of hydrodynamics differential calculations were needed for the implosion weapon's development, but employing hand computing for the complex implosion calculations was not practical, particularly if a realistic equation of state were to be used. The IBM PCAM equipment offered a solution.…”