Editing John von Neumann (section)

=== Fluid dynamics ===
Von Neumann made fundamental contributions in the field of [[fluid dynamics]], including the classic flow solution to [[blast wave]]s,<ref>{{harvc |last1=von Neumann |first1=John |year=1976 |chapter=The Point Source Solution |in=Taub |pages=219–237}}</ref> and the co-discovery (independently by [[Yakov Borisovich Zel'dovich]] and [[Werner Döring]]) of the [[ZND detonation model]] of explosives.<ref>{{harvc |last1=von Neumann |first1=John |year=1976 |chapter=Theory of Detonation Waves. Progress Report to the National Defense Research Committee Div. B, OSRD-549 |orig-year=1942 |url=https://web.archive.org/web/20160610184551/http://www.geocities.jp/nomonomo2007/ReadingPhysics/von_Neumann/Detonation.pdf |access-date=June 10, 2016 |in=Taub |pages=205–218}}</ref> During the 1930s, von Neumann became an authority on the mathematics of [[shaped charges]].<ref>{{cite book |title=Ballistics: Theory and Design of Guns and Ammunition |edition=2nd |first1=Donald E. |last1=Carlucci |first2=Sidney S. |last2=Jacobson |publisher=CRC Press |date=26 August 2013 |page=523}}</ref>

Later with [[Robert D. Richtmyer]], von Neumann developed an algorithm defining ''artificial [[viscosity]]'' that improved the understanding of [[shock wave]]s. When computers solved hydrodynamic or aerodynamic problems, they put too many computational grid points at regions of sharp discontinuity (shock waves). The mathematics of artificial viscosity smoothed the shock transition without sacrificing basic physics.<ref>{{cite journal |title=A Method for the Numerical Calculation of Hydrodynamic Shocks |last1=von Neumann |first1=J. |last2=Richtmyer |first2=R. D. |author-link2=Robert D. Richtmyer |journal=Journal of Applied Physics |volume=21 |issue=3 |pages=232–237 |date=March 1950 |doi=10.1063/1.1699639 |bibcode=1950JAP....21..232V }}</ref>

Von Neumann soon applied computer modelling to the field, developing software for his ballistics research. During World War II, he approached R. H. Kent, the director of the US Army's [[Ballistic Research Laboratory]], with a computer program for calculating a one-dimensional model of 100 molecules to simulate a shock wave. Von Neumann gave a seminar on his program to an audience which included his friend [[Theodore von Kármán]]. After von Neumann had finished, von Kármán said "Of course you realize [[Joseph-Louis Lagrange|Lagrange]] also used digital models to simulate [[continuum mechanics]]." Von Neumann had been unaware of Lagrange's {{lang|fr|[[Mécanique analytique]]}}.<ref name=mhr1980>{{cite book |editor1-last=Metropolis |editor1-first=Nicholas |editor1-link=Nicholas Metropolis |editor2-first=J. |editor2-last=Howlett |editor2-link=Jack Howlett |editor3-first=Gian-Carlo |editor3-last=Rota |editor3-link=Gian-Carlo Rota |title=A History of Computing in the Twentieth Century  |publisher=Elsevier |year=1980 |doi=10.1016/C2009-0-22029-0 |isbn=978-1-4832-9668-5 |pages=24–25}}</ref>