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Theory and Structure of the AFTON Codes

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Final rept. 12 Nov 1964-8 Apr 1966

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A procedure for writing finite difference analogs of the principles of continuum mechanics is presented. The method leads to analogs of the integral statements of mass and momentum conservation, and the first law of thermodynamics, which are exact under two simple discretization assumptions, and which imply an exactly conservative finite difference equation for the total energy. The method and the equations which follow from it apply to general systems of continuous media, hydrodynamic or otherwise. The finite difference equations form the basis of a set of computer codes for the calculation of motion described by one and two spatial coordinates. The codes permit the use of arbitrary time dependent coordinate systems to solve specific problems. The AFTON I code, which deals with linear, cylindrical, and spherical one- dimensional systems, has been expanded to include general stresses and strains. Some preliminary attempts have been made to define an optimum coordinate mesh to describe continuum motion, and specific problems have been solved by AFTON I using these coordinate systems. For spherically diverging waves in an elastic medium, the solutions obtained have been more accurate than those given by numerical Lagrangian methods with the same number of mesh points, although some shock front erosion is evident, apparently as a result of deficiencies in the coordinate systems employed.

Subject Categories:

  • Numerical Mathematics
  • Computer Programming and Software
  • Mechanics

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