Flux vector splitting and approximate Newton methods
Abstract
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocitysound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasionedimensional flow in a nozzle. Results are given for steady flows with shocks.
 Publication:

6th Computational Fluid Dynamics Conference
 Pub Date:
 1983
 Bibcode:
 1983cfd..conf..535J
 Keywords:

 Computational Fluid Dynamics;
 Euler Equations Of Motion;
 Iterative Solution;
 Newton Methods;
 NewtonRaphson Method;
 Nozzle Flow;
 Dirichlet Problem;
 Eigenvalues;
 Fourier Analysis;
 Nonlinear Systems;
 Numerical Stability;
 One Dimensional Flow;
 Shock Waves;
 Steady Flow;
 Fluid Mechanics and Heat Transfer