The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 41
Inrush problem with Dirichlet boundaries at x = −5 and x = 5.
An inrush problem with Dirichlet boundaries at x = −5 and x = 5, from time t = 0 to t = 10. The initial conditions are (ρl, ul, pl) = (0.1, 0.0, 0.2) and (ρr, ur, pr) = (0.1, 0.0, 0.2). The boundary values are (ρl, ul, pl) = (0.3, 0.6, 0.4) and (ρr, ur, pr) = (0.6, −0.6, 0.5). The maximum error metric is (Δmax ρ, Δmax u, Δmax p) = (1.0e-4, 1.0e-3, 1.0e-3). Two asymmetrical shocks propagate in from the edges, cross near the center, and continue to the opposite edges, where they are squelched by the boundary conditions.