Table 3
Comparison of the performance of the JFNK+PBP method presented in this paper with the Broyden methods presented in Viallet et al. (2013), for the 2D red giant test case.
| Method | CFLhydro | CFLadv | CFLrad |
|
|
|
|
|
||||||
| CFL adv,max = 0.5 | ||||||
| Broyden(10-2)+ILU(1) | 17.7 | 0.46 | 4.8 | 7.3 | 4.0 | 227 |
| JFNK(10-1)+ PBP | 18.9 | 0.49 | 4.9 | 6.2 | 7.2 | 202 |
| JFNK(10-2)+ PBP | 18.9 | 0.49 | 4.9 | 4.6 | 18.4 | 161 |
| JFNK(10-4)+PBP | 18.9 | 0.49 | 4.9 | 4.6 | 37.8 | 80 |
|
|
||||||
| CFL adv,max = 1 | ||||||
| Broyden(10-1)+ILU(1) | 37.9 | 0.93 | 8.2 | 9.5 | 4.3 | 382 |
| JFNK(10-1)+PBP | 40.2 | 0.98 | 8.6 | 6.6 | 18.5 | 200 |
| JFNK(10-2)+PBP | 40.0 | 0.98 | 8.5 | 5.7 | 41.3 | 124 |
| JFNK(10-4)+PBP | 40.0 | 0.98 | 8.5 | 5.7 | 200.7 | 32 |
|
|
||||||
| CFL adv,max = 1.5 | ||||||
| Broyden(10-1)+ILU(1) | 45.2 | 1.10 | 9.6 | 13.2 | 4.9 | 383 |
| JFNK(10-1)+PBP | 55.2 | 1.42 | 11.0 | 8.9 | 37.8 | 121 |
| JFNK(10-2)+PBP | 55.8 | 1.43 | 11.0 | 7.8 | 79.3 | 73 |
| JFNK(10-4)+PBP | 55.7 | 1.43 | 11.0 | 7.7 | 252.0 | 33 |
Notes. The value of the linear tolerance η is given in parenthesis after the name of the method; ILU(k) refers to an incomplete LU factorization of order k; PBP refers to physics-based preconditioning for sound waves only.
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