Rezone algorithms for the Lagrangian gasdymanics
Principle ideas of our methodology
- Arbitrary Lagrangian-Eulerian (ALE) simulation.
- Error-Minimization-Based (EMB) rezone strategy (know-how).
- Algorithms for generating adaptive smooth grids.
Example I: Sod's shock tube
We consider the Sod's shock tube problem.
The problem consists of two regions of gas with γ = 1.4
initially separated by a membrane at x = 0.5. The gas to the left
of the membrane is more dense (&rhoL = 1 and
&rhoR = 0.125) and at a higher pressure
(pL = 1 and pR = 0.1) compared to the
one on the right. We impose the reflecting boundary conditions at
x = 0 and x = 1.
The left picture shows the trajectories of the Lagrangian points (blue
lines) and the pressure profile (red line). Each horizontal slice
represents positions of mesh points at the corresponding time moment.
The right picture shows the same data for the EMB rezone strategy.
We observe more accurate solution with a sharp shock profile.
Moreover, the adaptive strategy requires less time integration steps (2829 vs 3800).
