The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics
Figure 19
Panel A shows a fluid divided into three cells c1, c2, c3 of widths 2, 1, and 3 from left to right (hence the name “213 problem”). All three cells were created at time t = 0, and all three have density ρ = 1, pressure p = 1, and velocity u = 0. In a simulation without wavefront unioning, if wavefront w23 chopped out a new cell at time t = 2.5, that new cell would have a net momentum of −0.5. Panel B shows that this is because the rightward momentum Ppr from c1 levels off at t = 2.0, while the leftward momentum from c3 continues to increase until t = 3.0. This demonstrates that wavefront unioning is required to avoid unphysical changes in cell velocity during simulation.