Eulerian and Lagrangian simulations of continuum flow problems are commonplace.
Using particles to solve some of these problems became a viable approach
when the smooth particle methods were discovered by Lucy and Monaghan.
Jeff Swegle (Sandia, Albuquerque) and Charles Wingate (Los Alamos Laboratory)
have implemented the method for a variety of interesting applications.
A particularly challenging problem, free expansion within an enclosure, can be
treated with smooth-particle methods [Hoover and Posch in Physical Review E
59, 1770 (1999)]. Carol and I wrote a pedagogical description of the method,
"SPAM-Based Recipes for Continuum Simulations"
[Computing in Science and Engineering 3(2), 78 (2001)].
During the summer of 2003 we worked with a
Livermore High School senior, Elizabeth Merritt (now at Mount Holyoke), on
new methods for conserving angular momentum and delaying solid-phase tensile
instability using SPAM. See the list of Recent Publications on the Main
Page. During 2004-2006 Carol and I wrote a comprehensive account,
Applied Mechanics---The State of the Art], published in 2006 by
World Scientific Publishing in Singapore. The book has so far inflated from
$75 to $100, as of 2010. For any researcher who is seriously interested in this work
but cannot afford to buy it, we would be happy to honor a request for a free hard
copy. The smooth particle techniques open many interesting research areas and
introduce a simple and transparent way to solve hard problem in continuum
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