Use of the method of parallel chords for solving difference equations of hydrodynamics
Abstract
It is shown that the method of parallel chords, a modification of the Newton method, can be used to solve the difference equations of hydrodynamics, written in a Lagrangian form. Compared to the classical Newton method, the modified method has the following advantages: (1) single computation of the linearsystem matrix makes it possible to reduce computations by one iteration; (2) matrix symmetry makes it possible to reduce the size of the memory; and (3) the positive and selfadjoint character of the linearsystem operator removes several difficulties and reduces the time of solution of the system.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 June 1981
 Bibcode:
 1981ZVMMF..21..707G
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Hydrodynamic Equations;
 Lagrange Coordinates;
 Numerical Integration;
 Boundary Value Problems;
 Iterative Solution;
 Linear Equations;
 Newton Methods;
 Newton Theory;
 Nonlinear Equations;
 Two Dimensional Flow;
 Two Phase Flow;
 Fluid Mechanics and Heat Transfer