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Advances in Aerodynamics

Table 2 Accuracy test for adaptive SDC-LDG scheme of 2D NS equations

From: Adaptive local discontinuous Galerkin methods with semi-implicit time discretizations for the Navier-Stokes equations

Re∞

k

N

\(\phantom {\dot {i}\!}\|\rho - \rho _{h}\|_{L^{2}}\)

Order

\(\phantom {\dot {i}\!}\|\mathbf {u}-\mathbf {u}_{h}\|_{L^{2}}\)

Order

\(\phantom {\dot {i}\!}\|p-p_{h}\|_{L^{2}}\)

Order

200

1

16

4.96E-03

–

2.68E-02

–

8.81E-03

–

  

32

1.04E-03

2.25

6.16E-03

2.12

1.81E-03

2.27

  

64

2.34E-04

2.15

1.44E-03

2.09

4.10E-04

2.14

  

128

5.61E-05

2.06

3.52E-04

2.03

9.87E-05

2.05

 

2

16

6.56E-04

–

3.15E-03

–

1.12E-03

–

  

32

8.51E-05

2.94

3.81E-04

3.04

1.39E-04

3.01

  

64

1.07E-05

2.99

4.76E-05

3.00

1.75E-05

2.99

  

128

1.28E-06

3.06

5.95E-06

3.00

2.16E-06

3.02

1000

1

16

4.51E-03

–

2.39E-02

–

8.05E-03

–

  

32

1.03E-03

2.11

5.84E-03

2.03

1.81E-03

2.14

  

64

2.50E-04

2.05

1.40E-03

2.05

4.38E-04

2.05

  

128

6.20E-05

2.01

3.46E-04

2.02

1.08E-04

2.01

 

2

16

6.68E-04

–

3.30E-03

–

1.22E-03

–

  

32

8.47E-05

2.97

3.97E-04

3.05

1.51E-04

3.01

  

64

1.08E-05

2.96

4.86E-05

3.02

1.90E-05

2.99

  

128

1.36E-06

3.00

6.02E-06

3.01

2.37E-06

3.00

5000

1

16

4.51E-03

–

2.39E-02

–

8.10E-03

–

  

32

1.03E-03

2.12

5.83E-03

2.03

1.82E-03

2.15

  

64

2.50E-04

2.05

1.40E-03

2.05

4.39E-04

2.05

  

128

6.19E-05

2.01

3.46E-04

2.01

1.08E-04

2.01

 

2

16

6.93E-04

–

3.65E-03

–

1.27E-03

–

  

32

8.67E-05

3.00

4.44E-04

3.03

1.56E-04

3.02

  

64

1.06E-05

3.02

5.18E-05

3.09

1.94E-05

3.00

  

128

1.35E-06

2.98

6.24E-06

3.05

2.43E-06

3.00

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