Table 2: Errors in the shock tube problems 3 and 6 for HLLE and Roe's approximate Riemann solvers, and Tadmor's central scheme using two different third order spatial reconstructions (CFL = 0.5 and N_x=400).
Test Scheme L₁ (10^-2) $L_{\infty}$ (10^-3)

PPM PHM PPM PHM

Problem 3 HLLE 3.37 2.81 2.87 0.67

Roe 3.39 2.95 3.44 1.31

Tadmor 3.41 3.41 2.58 1.04

Problem 6 HLLE 22.0 21.7 3.53 1.20

Roe 21.7 21.6 2.63 1.20

Tadmor 25.2 22.4 0.92 2.69

**Table 2:** Errors in the shock tube problems 3 and 6 for HLLE and Roe's approximate Riemann solvers, and Tadmor's central scheme using two different third order spatial reconstructions (CFL = 0.5 and N_x=400).
Test	Scheme	L₁ (10^-2)	$L_{\infty}$ (10^-3)
		PPM	PHM	PPM	PHM
Problem 3	HLLE	3.37	2.81	2.87	0.67
	Roe	3.39	2.95	3.44	1.31
	Tadmor	3.41	3.41	2.58	1.04
Problem 6	HLLE	22.0	21.7	3.53	1.20
	Roe	21.7	21.6	2.63	1.20
	Tadmor	25.2	22.4	0.92	2.69

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