The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 31
Toro’s test problem 5, with initial conditions (ρl, ul, pl) = (1.0, −19.59745, 1000.0) and (ρr, ur, pr) = (1.0, −19.59745, 0.01), with maximum error metric (Δmax ρ, Δmax u, Δmax p) = (1.0e-5, 1.0e-2, 1.0e-2), at time t = 0.03. The initial values of this test were designed to give an almost stationary contact at the origin, which causes difficulties for some numerical methods. RRM handles stationary contacts the same as it does moving contacts, due to the Lagrangian nature of the simulation.