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Table 1 Example 1. L∞ errors and numerical orders of temporal accuracy obtained with the GSA 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

7.59E−03

 

7.16E−05

 

1.23E−03

 

80

3.03E−03

1.32

8.78E−06

3.03

9.95E−05

3.63

160

6.37E−04

2.25

1.17E−06

2.90

1.31E−05

2.92

320

9.85E−05

2.69

1.48E−07

2.99

6.58E−07

4.32

640

1.28E−05

2.94

1.95E−08

2.93

8.75E−09

6.23