The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics

doi:10.1371/journal.pone.0039999

The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics

Figure 23

Test 1: Sod’s test problem at high accuracy.

Sod’s problem with initial conditions (ρ_l, u_l, p_l) = (1.0, 0.0, 1.0) and (ρ_r, u_r, p_r) = (0.125, 0.0, 0.1), with maximum error metric (Δ_{max ρ}, Δ_{max u}, Δ_{max p}) = (1.0e-5, 1.0e-3, 1.0e-3), at time t = 1.5. This test shows typical RRM results: an s-shaped contact because RRM is not adiabatic across contacts, and a slight peak at the shock due to finite shock thickness.

doi: https://doi.org/10.1371/journal.pone.0039999.g023