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version 0.6.0
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version 0.6.0
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This page demonstrates the spatial convergence rates of diffusion schemes.
A 2D cavity of unit length is used and the spatial mesh is reduced, at constant time step, for testing convergence. The schemes are verified in
In order to suppress most temporal errors, the most precise temporal scheme has to be used.
The precise spatial convergence analysis is somehow complex as temporal errors also occurs and cannot be completely removed. Hence, we have chosen numerical parameters such that the effective schemes' convergence rate appear in the range. Absolute values of error can be compared between schemes.
All schemes exhibit the expected convergence rate.
All schemes exhibit the expected convergence rate.
| Mesh | Temperature L1 error | order | Temperature L2 error | order | Temperature Linf error | order |
|---|---|---|---|---|---|---|
| 32×4 | 1.2935846888020158e-07 | n/a | 1.4275968501959712e-07 | n/a | 1.9801337136637898e-07 | n/a |
| 64×8 | 3.230845164493845e-08 | 2.001 | 3.5828048794521865e-08 | 1.994 | 5.042452899672867e-08 | 1.973 |
| 128×16 | 8.075433294014566e-09 | 2.000 | 8.965949536945098e-09 | 1.999 | 1.2664493231895335e-08 | 1.993 |
| 256×32 | 2.019007121605303e-09 | 2.000 | 2.2423279166181104e-09 | 1.999 | 3.1701760105917742e-09 | 1.998 |
| 512×64 | 5.050139275168642e-10 | 1.999 | 5.609153766074666e-10 | 1.999 | 7.931948431405544e-10 | 1.999 |
| 1024×128 | 1.2652285164893096e-10 | 1.997 | 1.4053067184465362e-10 | 1.997 | 1.9873691581295816e-10 | 1.997 |
| 2048×256 | 3.190051783580694e-11 | 1.988 | 3.543250949391376e-11 | 1.988 | 5.010980519415398e-11 | 1.988 |
| 4096×512 | 8.243448220815388e-12 | 1.952 | 9.156162657506196e-12 | 1.952 | 1.294897522541305e-11 | 1.952 |
| Mesh | Temperature L1 error | order | Temperature L2 error | order | Temperature Linf error | order |
|---|---|---|---|---|---|---|
| 32×4 | 1.2935811613719317e-07 | n/a | 1.4275929581424112e-07 | n/a | 1.98012831797989e-07 | n/a |
| 64×8 | 3.230809235031315e-08 | 2.001 | 3.5827650431421577e-08 | 1.994 | 5.042396944432426e-08 | 1.973 |
| 128×16 | 8.075072590793802e-09 | 2.000 | 8.965549007459253e-09 | 1.999 | 1.2663928239398103e-08 | 1.993 |
| 256×32 | 2.018646414562726e-09 | 2.000 | 2.2419273306497303e-09 | 2.000 | 3.1696093527600055e-09 | 1.998 |
| 512×64 | 5.046539177145401e-10 | 2.000 | 5.605155005289335e-10 | 2.000 | 7.926290734872055e-10 | 2.000 |
| 1024×128 | 1.2616297654602127e-10 | 2.000 | 1.4013095327324698e-10 | 2.000 | 1.9817114615960918e-10 | 2.000 |
| 2048×256 | 3.154069960819504e-11 | 2.000 | 3.503284918082218e-11 | 2.000 | 4.954359145159515e-11 | 2.000 |
| 4096×512 | 7.885168823422693e-12 | 2.000 | 8.758216893810434e-12 | 2.000 | 1.2386203174230559e-11 | 2.000 |
| Mesh | Temperature L1 error | order | Temperature L2 error | order | Temperature Linf error | order |
|---|---|---|---|---|---|---|
| 32×4 | 2.636976562456206e-09 | n/a | 2.910160810021556e-09 | n/a | 4.0365091269478626e-09 | n/a |
| 64×8 | 1.657192965753146e-10 | 3.992 | 1.8377232667874604e-10 | 3.985 | 2.5864177466417004e-10 | 3.964 |
| 128×16 | 1.0371753748818907e-11 | 3.998 | 1.151550938092588e-11 | 3.996 | 1.626543344457332e-11 | 3.991 |
| 256×32 | 6.484509110227243e-13 | 4.000 | 7.201783604850409e-13 | 3.999 | 1.018185535883731e-12 | 3.998 |
| 512×64 | 4.04939923010373e-14 | 4.001 | 4.4971269538839685e-14 | 4.001 | 6.361577931102147e-14 | 4.000 |
| 1024×128 | 2.5002769359029273e-15 | 4.018 | 2.784012498112694e-15 | 4.014 | 4.3298697960381105e-15 | 3.877 |
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