The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 6
Sod’s shock tube problem time evolution from t = 0 to t = 1.5 seconds.
Sod’s shock tube problem showing density ρ, velocity u, and pressure p from time t = 0 to time t = 1.5 seconds. We can see three flow features: an expansion fan, a contact, and a shock. The contact and the shock both start at the origin and move to the right, with the shock running ahead due to its higher speed. The expansion fan gradually slopes left as more and more fluid flows to the right to feed the shock.