The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 42
Rightward flow problem with far-field boundaries at x = −5 and x = 5.
A rightward flow problem with free boundaries at x = −5 and x = 5, from time t = 0 to t = 15. The initial conditions are (ρl, ul, pl) = (0.8, 0.8, 0.1) and (ρr, ur, pr) = (0.1, 0.7, 0.05). The maximum error metric is (Δmax ρ, Δmax u, Δmax p) = (5.0e-5, 1.0e-4, 1.0e-4). Fast-moving fluid flows in from the left boundary and pushes the slower fluid in front of it, forcing it out of the right boundary. After about t = 14 all of the fluid is in the left state, since all the right fluid as been pushed out.