Integrated gradients: A derivation of some difference forms for the equation of motion for compressible flow in twodimensional Lagrangian hydrodynamics, using integration of pressures over surfaces
Abstract
This paper describes a method of deriving gradients (that is, accelerations) for difference calculations of the equations of motion (momentum conservation) in twodimensional Lagrangian meshes in an rz coordinate system. The method basically considers various ways of defining the masses associated with each vertex and methods of integrating pressures over the surfaces of those masses, and then combining them in various ways to conserve momentum transfer between vertices. These gradients are derived analytically for planes, cylinders, and spheres to test for uniform motion. All results described have been tested with actual numerical calculations.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1986
 Bibcode:
 1986STIN...8631020B
 Keywords:

 Compressible Flow;
 Equations Of Motion;
 Hydrodynamics;
 Integrals;
 Numerical Analysis;
 Pressure Gradients;
 Fluid Mechanics and Heat Transfer