FreeLagrange methods for compressible hydrodynamics in two space dimensions
Abstract
Since 1970 a research and development program in FreeLagrange methods has been active at Livermore. The initial steps were taken with incompressible flows for simplicity. Since then the effort has been concentrated on compressible flows with shocks in two space dimensions and time. In general, the line integral method has been used to evaluate derivatives and the artificial viscosity method has been used to deal with shocks. Basically, two FreeLagrange formulations for compressible flows in two space dimensions and time have been tested and both will be described. In method one, all prognostic quantities were node centered and staggered in time. The artificial viscosity was zone centered. One mesh reconnection philosphy was that the mesh should be optimized so that nearest neighbors were connected together. Another was that vertex angles should tend toward equality. In method one, all mesh elements were triangles. In method two, both quadrilateral and triangular mesh elements are permitted. The mesh variables are staggered in space and time as suggested originally by Richtmyer and von Neumann. The mesh reconnection strategy is entirely different in method two. In contrast to the global strategy of nearest neighbors, we now have a more local strategy that reconnects in order to keep the integration time step above a user chosen threshold. An additional strategy reconnects in the vicinity of large relative fluid motions. Mesh reconnection consists of two parts: (1) the tools that permits nodes to be merged and quads to be split into triangles etc. and; (2) the strategy that dictates how and when to use the tools. Both tools and strategies change with time in a continuing effort to expand the capabilities of the method. New ideas are continually being tried and evaluated. <The successful ones stay in the code, and in some sense its intelligence increases with time.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1985
 Bibcode:
 1985STIN...8616523C
 Keywords:

 Compressible Flow;
 EulerLagrange Equation;
 Hydrodynamics;
 Mathematical Models;
 Computer Programs;
 Fluid Dynamics;
 Viscosity;
 Fluid Mechanics and Heat Transfer