New fast superdashpot timedependent techniques for the numerical simulation of steady flows. I
Abstract
This paper describes new fast artifical timedependent methods leading asymptotically, after a sufficiently long time, to the solution of any steady system of firstorder equations. They can, namely, be very useful and efficient for computing steady inviscid transonic mixed flows, as well as for solving the steady hybrid equations of subsonic rotational flows. The timedependent equations used by the new methods are constructed by adding a purely artificial unsteady operator to the steady physical equations. That operator introduces a strong internal damping of the perturbation waves similar to that due to dashpots on the surface of a vibrating membrane. As a result, a very large rate of convergence of the same order of magnitude as that of the overrelaxation techniques is obtained. The new methods can be applied to any conservative finite differences, finite volumes or finite element discretization of the steady equations. Their level of generality is comparable to that of the classical timedependent techniques using the unsteady Euler equations, but they are much faster.
 Publication:

Computers and Fluids
 Pub Date:
 September 1980
 Bibcode:
 1980CF......8..351E
 Keywords:

 Computational Fluid Dynamics;
 Computerized Simulation;
 Inviscid Flow;
 Steady Flow;
 Subsonic Flow;
 Transonic Flow;
 Boundary Value Problems;
 Euler Equations Of Motion;
 Finite Difference Theory;
 Finite Element Method;
 Operators (Mathematics);
 Time Dependence;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer