Local time Stepping
 

Hi,

I have question concerning local time stepping. First of all, I will write a small introduction so everyone can understand what I am talking about.

For local time stepping, the time-step Dt depends on the current grid-cell:

dt=C*dx_(i,j,k)/(|c| + a)

dx = grid spacing c = velocity a = velocity of sound

I know that dt is not constant. But I have problems to understand how the local time step influences the differential equation system in a steady simulation - since Q^(n+1) = Q^(n).

J*dQ/dt + dE/dx_1 + dF/dx_2 + dG/dx_3 = 0