PLM tests

What happens if we look at the same two high mach number tests from the previous posts (the square wave test and the shock tube test), but use a piecewise linear reconstruction?

Figure 1a: PLMC, exact solver, no dual energy, $v \approx 800 c_s$

Figure 1b: Same as Figure 1a but with dual energy

Figure 2a: PLMP, exact solver, no dual energy, $v \approx 800 c_s$

Figure 2b: Same as Figure 2a but with dual energy

Figure 3a: PLMC, exact solver, no dual energy, $v \approx 100 c_s$

Figure 3b: Same as Figure 3a but with dual energy

Figure 4a: PLMP, exact solver, no dual energy, $v \approx 100 c_s$

Figure 4b: Same as Figure 4a but with dual energy