The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 32
Sod’s test problem at high accuracy, showing cell density.
Sod’s problem with initial conditions (ρl, ul, pl) = (1.0, 0.0, 1.0) and (ρr, ur, pr) = (0.125, 0.0, 0.1), with maximum error metric (Δmax ρ, Δmax u, Δmax p) = (1.0e-5, 1.0e-3, 1.0e-3), at time t = 1.5. Each of the approximately 800 cells is shown by a single dot, except the two edge cells which have two dots apiece. This figure shows that RRM is good at concentrating cells (and thereby computational effort) in areas of primitive variable gradient.