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Table 3 Example 1. L∞ errors and numerical orders of temporal accuracy obtained with the SA IMEX-ARS3 WCNS at t=0.1

From: High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

N

ε=0.01

ε=0.1

ε=1

 

L∞ error

Order

L∞ error

Order

L∞ error

Order

40

7.90E−03

 

9.18E−05

 

6.50E−04

 

80

3.34E−03

1.24

1.09E−05

3.07

9.50E−05

2.78

160

7.45E−04

2.16

1.40E−06

2.97

1.71E−05

2.47

320

1.19E−04

2.65

1.75E−07

3.00

1.97E−07

6.44

640

1.57E−05

2.92

2.19E−08

3.00

6.74E−10

8.19