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Table 3 1-D accuracy test: errors and convergence orders of 6th-order compact nonlinear schemes with Δt=0.3Δx3/2

From: Compact higher-order gas-kinetic schemes with spectral-like resolution for compressible flow simulations

mesh length

L1 error

Order

L2 error

Order

L∞ error

Order

1/5

7.495e-003

 

8.448e-003

 

1.248e-002

 

1/10

3.624e-004

4.37

4.307e-004

4.29

7.357e-004

4.08

1/20

7.877e-006

5.52

8.677e-006

5.63

1.461e-005

5.65

1/40

4.216e-008

7.55

5.440e-008

7.32

1.235e-007

6.89

1/80

2.119e-010

7.64

2.647e-010

7.68

7.407e-010

7.38

1/160

2.100e-012

6.66

2.279e-012

6.86

3.540e-012

7.71