一个关于超音速钝体的问题

ydavid

一个关于超音速钝体的问题
In supersonic blunt body problem, the sudden change in nature of the Euler equations across the sonic line cause the flow region seperating into subsonic and supersonic region, which have totally different mathematical behavior of elliptic and hyperbolic equations.
To tackle this problem, Moretti and Abbett in 1966 use time as an additional indepent variable, the governing Euler equations become hyperbolic with respect to time, thus allowing a straightforward marching solution in time.
My question is:
How can we make sure that the proper steady flow results appearing in the limit of large times?

newcfd

As I know, without time variable you can solve the Euler equations too by using Newton Method.
However, higher damping is needed to stabilize the Newton Method. Problem is that higher order
resolution (second order) is hard to obtain on unstructured mesh. The introduction of time
variable made it possible to solve Euler Equation by using explicit method with small time steps.
Once the residuals are below some prescribed tolerance (often 10^-4, can be 10^-3 by industrial
design), it is believed that a steady solution is obtained. Kind of like, the time goes to infinite,
the first term with time disappears.