It is well known that in solving steady state problems using hyperbolic time-stepping methods the intent is to drive the transients to zero as quickly as possible. In this paper the convergence to steady state of the Lax-Wendroff method applied to solving the equations of gas dynamics is analyzed for the Laval nozzle problem by comparing the relative rates of damping and convection using a linearized eigenmode analysis. This analysis is developed for the simpler isenthalpic system and then extended to the full Euler equations. Finally, this allows a comparison between these systems. For both models, useful analytical information can be gleaned about the transient behavior of these systems, especially in regard to quantifying the competitive factors affecting the removal of unsteady waves.
SIAM Journal on Scientific Computing
(1999). Importance of Convection and Damping on Rates of Convergence for the Lax-Wendroff Method. SIAM Journal on Scientific Computing, 20(4), 1513-1529.
Available at: http://aquila.usm.edu/fac_pubs/4616