PMC

a, b, c Shock wave dynamics for “pushing" piston (white curves show qualitatively the density): (a) compressing piston producing a shock wave in an ideal (non-dispersive) fluid; (b) shock-shock produced via stepwise initial velocity profile (Riemann problem); (c) DSW-DSW via Riemann problem in a dispersive photon fluid; d,e,f: Rarefaction wave dynamics for “retracting" pistons: (d) single RW; (e) RW-RW from the Riemann problem; (f) similar RW-RW in a dispersive photon fluid.

Schematic diagram of the fluid and solid dynamics two-way coupling in a fluid–structure interaction problem (adapted from []). (Online version in colour.)

Sketch of eye-shaped domain problem for modeling fluid dynamics of the tear film over the exposed ocular surface during the interblink period.

A rightward flow problem with free boundaries at x = −5 and x = 5, from time t = 0 to t = 15. The initial conditions are (ρ _l, u _l, p _l) = (0.8, 0.8, 0.1) and (ρ _r, u _r, p _r) = (0.1, 0.7, 0.05). The maximum error metric is (Δ_{max ρ}, Δ_{max u}, Δ_{max p}) = (5.0e-5, 1.0e-4, 1.0e-4). Fast-moving fluid flows in from the left boundary and pushes the slower fluid in front of it, forcing it out of the right boundary. After about t = 14 all of the fluid is in the left state, since all the right fluid as been pushed out.