The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 25
Test 3: Modified Sod’s test problem with initial u = 1.0.
A modified version of Sod’s problem where the entire fluid moves right with u = 1.0, with initial conditions (ρl, ul, pl) = (1.0, 1.0, 1.0) and (ρr, ur, pr) = (0.125, 1.0, 0.1), with maximum error metric (Δmax ρ, Δmax u, Δmax p) = (5.0e-5, 1.0e-3, 1.0e-3), at time t = 1.5. This test shows one of the benefits of the fully Lagrangian nature of RRM. Since the cells all move to the right with u = 1.0, the shock front does not have to cross cell edges during the simulation, so the shock is just as sharp as in the u = 0 case.