ETS Verification and Validation (VV)
Roadmap for the ETS verification and benchmarking procedure
(based on G. Pereverzev's proposal)
- Proposal for ETS verification and benchmarking procedure (PDF)
- ETS verification and benchmarking (ASTRA results) (PDF)
Results obtained in 2011 for UAL-version 4.08b
NOTE: For the particle diffusion coefficient D and pinch velocity v, the values below correspond in fact to the individual coefficients for each of the three transport models considered within ETS. For example, a v=1 translates into an effective pinch velocity of 3 in the density transport equation and of 0+3/2+5/2=4 in the ion flux contributing to heat transport.
| Case | Description | Subcase | Solver | Comments | Graphic output (PDF) |
|---|---|---|---|---|---|
| I.1.1 | Constant densities and temperatures | N/A | 3 | Convergence ok. Errors within machine precision | I.1.1_s3 |
| 7 | Convergence ok. Errors within machine precision | I.1.1_s7 | |||
| 10 | Convergence ok. Errors within machine precision | I.1.1_s10 | |||
| I.1.2 | Interpretative time-dependent solution for densities | N/A | 3 | Under analysis: no time evolution for the temperatures | I.1.2_s3 |
| I.1.3 | Conservation laws (particle and energy) with diffusion | N/A | N/A | This case was treated under I.1.5 | N/A |
| I.1.4 | Conservation laws (particle and energy) with discontinuous diffusion coefficient | N/A | 3 | Convergence ok | I.1.4_s3 |
| 7 | Convergence ok | I.1.4_s7 | |||
| 10 | Failed to initiate | ||||
| I.1.5 | Conservation laws (particle and energy) with diffusion and convection | D=0.1 and v=0 | 3 | Convergence in density reached; asymptotic solution (for density) reached; convergence in temperature never fully reached | I.1.5_s3_101pts_1e-3s
I.1.5_s3_51pts_1e-3s I.1.5_s3_101pts_1e-2s |
| 7 | I.1.5_s7_101pts_1e-3s
I.1.5_s7_51pts_1e-3s I.1.5_s7_101pts_1e-2s |
||||
| 10 | |||||
| I.1.5.a
D=0.1 and v=0.1 |
3 | Solvers 3 and 7: Convergence in temperature reached; convergence in density reached; asymptotic solution never reached (after 50s and 100s). Solver 10: does not converge (number of iterations exceeds 1000). | I.1.5.a_s3_101pts_1e-3s
I.1.5.a_s3_51pts_1e-3s I.1.5.a_s3_101pts_1e-2s |
||
| 7 | I.1.5.a_s7_101pts_1e-3s | ||||
| 10 | |||||
| I.1.5.b
D=0.1 and v=0.3 |
3 | No convergence for both density and temperature (worse for density);
deviation from asymptotic solution increases with time. Errors are similar for solvers 3 and 7;
the latter reduces the energy error with time, at short time-steps.
Increasing number of points reduces deviation from asymptotic solution (tested for solver 3)
Neither solver yields zero steady-state particle- and energy- flux. The on-axis behavior of Te is different for solvers 3 and 7. Convergence proceeds through decreasing (solver 3 and solver 7 at long time-steps) and increasing (solver 7 at short time-steps) fluxes near the wall |
I.1.5.b_s3_101pts_1e-3s
I.1.5.b_s3_51pts_1e-3s I.1.5.b_s3_101pts_1e-2s |
||
| 7 | I.1.5.b_s7_101pts_1e-3s
I.1.5.b_s7_51pts_1e-3s I.1.5.b_s7_101pts_1e-2s |
||||
| 10 | Failed to initiate | ||||
| I.1.5.c
D=0.1 and v=1.0 |
3 | Solvers 3 and 7: For v>1 the number of iterations exceeds the max value of 1000,
apparently because ETS doesn't conserve the number of particles.
The situation is mitigated (not solved) by increasing Np and decreasing dt. Solver 10 fails to initiate. |
I.1.5.c_s3_101pts_1e-3s
I.1.5.c_s3_51pts_1e-3s I.1.5.c_s3_101pts_1e-2s |
||
| 7 | I.1.5.c_s7_101pts_1e-3s
I.1.5.c_s7_101pts_1e-2s |
||||
| 10 | |||||
| I.1.5.d
D=0.1 and v=2.0 |
3 | I.1.5.d_s3_501pts_1e-3s
I.1.5.d_s3_501pts_1e-4s |
|||
| 7 | |||||
| 10 | Failed to initiate | ||||
| I.1.5.h
D=0.1 and v=-0.1 |
3 | Solvers 3 and 7: Convergence in density and temperature reached; asymptotic solution (for density) almost always reached; Solver 10: fails to converge (number of iterations exceeds 1000). | I.1.5.h_s3_101pts_1e-3s
I.1.5.h_s3_51pts_1e-3s I.1.5.h_s3_101pts_1e-2s |
||
| 7 | I.1.5.h_s7_101pts_1e-3s
I.1.5.h_s7_101pts_1e-2s |
||||
| 10 | |||||
| I.1.5.i
D=0.1 and v=-0.3 |
3 | Convergence in density reached; convergence in temperature never fully reached; asymptotic solution never fully reached | I.1.5.i_s3_101pts_1e-3s
I.1.5.i_s3_51pts_1e-3s I.1.5.i_s3_101pts_1e-2s |
||
| 7 | I.1.5.i_s7_101pts_1e-3s
I.1.5.i_s7_51pts_1e-3s |
||||
| 10 | |||||
| I.1.5.j
D=0.1 and v=-1.0 |
3 | Solvers 3, 7, and 10 fail to converge (number of iterations exceeds 1000) long before the total exectution time of 4s (at best they go until 1.8s) | I.1.5.j_s3_101pts_1e-3s
I.1.5.j_s3_51pts_1e-3s I.1.5.j_s3_101pts_1e-2s |
||
| 7 | I.1.5.j_s7_101pts_1e-3s
I.1.5.j_s7_101pts_1e-2s |
||||
| 10 | I.1.5.j_s10_101pts_1e-3s
I.1.5.j_s10_51pts_1e-3s |
||||
| I.1.5.k
D=0.1 and v=-2.0 |
3 | No convergence for both density and temperature (worse for density); deviation from asymptotic solution increases with time | I.1.5.k_s3_101pts_1e-3s | ||
| 7 | |||||
| 10 |
Results obtained in 2012 for UAL-version 4.09a
NOTE: Solver 4 is the one with the best performance. Solvers 3, 7 and 10 are to be disregarded in the future.
ALL solvers fail to converge (i.e. demanding more than 1000 iterations) for convection v >= 1 m/s.
| Case | Description | Subcase | Solver | Comments | Graphic output (PDF) |
|---|---|---|---|---|---|
| I.1.1 | Constant densities and temperatures | N/A | 3 | Convergence ok.
Errors within machine precision, except for the on-axis value |
I.1.1_101pts_1e-2s |
| 4 | Convergence ok.
Errors within machine precision, except for the on-axis value |
||||
| 7 | NANs found | ||||
| 10 | Convergence ok.
Errors within machine precision |
||||
| I.1.2 | Interpretative time-dependent solution for densities
(D=0 and v=0) |
No external sources; no internal sources;
Te = Ti @ t=0 (no plasma collision source) |
4 | No time evolution for the pressure in the absence of all sources | I.1.2_101pts_1e-2s |
| I.1.2.a
No external sources; internal (convection) sources limited to 10%;
|
4 | Time evolution for the pressure due to internal sources | I.1.2.a_101pts_1e-2s | ||
| I.1.2.b
No external sources; no internal sources;
|
4 | Pressure evolves to constant values with time, due to e-i energy exchange | I.1.2.b_101pts_1e-2s | ||
| I.1.3 | Conservation laws (particle and energy) with diffusion | N/A | N/A | This case was treated under I.1.5 | N/A |
| I.1.4 | Conservation laws (particle and energy) with discontinuous diffusion coefficient | N/A | 3 | Convergence obtained; asymptotic solution (for density) reached. | I.1.4_101pts_1e-2s |
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained, with a problem on the axis. | ||||
| 10 | Convergence obtained, but for a very different asymptotic solution (for density). | ||||
| I.1.5 | Conservation laws (particle and energy)
with diffusion and convection
(D in m2/s; v in m/2) |
D=0.1 and v=0 | 3 | Convergence obtained; asymptotic solution (for density) reached. | I.1.5_101pts_1e-3s
I.1.5_51pts_1e-3s I.1.5_101pts_1e-2s |
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained, with a poor prediction of the asymptotic (density) solution and with a problem on the axis. | ||||
| 10 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| I.1.5.a
D=0.1 and v=0.1 |
3 | Convergence obtained; asymptotic solution (for density) reached; conservation laws poorly satisfied. | I.1.5.a_101pts_1e-3s
I.1.5.a_51pts_1e-3s I.1.5.a_101pts_1e-2s |
||
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained for 101 points only, with a poor prediction of the asymptotic (density) solution and with a problem on the axis; conservation laws poorly satisfied. | ||||
| 10 | Convergence obtained, but for a very different asymptotic solution (for density); conservation laws not satisfied. | ||||
| I.1.5.b
D=0.1 and v=0.3 |
3 | Convergence obtained; asymptotic solution (for density) reached; conservation laws poorly satisfied. | I.1.5.b_101pts_1e-3s
I.1.5.b_51pts_1e-3s I.1.5.b_101pts_1e-2s |
||
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained for 1e-2s only, with a poor prediction of the asymptotic (density) solution and with a problem on the axis; conservation laws poorly satisfied. | ||||
| 10 | Convergence obtained, but for a very different asymptotic solution (for density); conservation laws not satisfied. | ||||
| I.1.5.c
D=0.1 and v=1.0 |
3 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
I.1.5.c_101pts_1e-3s
I.1.5.c_51pts_1e-3s I.1.5.c_101pts_1e-2s |
||
| 4 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| 7 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| 10 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| I.1.5.h
D=0.1 and v=-0.1 |
3 | Convergence obtained; asymptotic solution (for density) reached. | I.1.5.h_101pts_1e-3s
I.1.5.h_51pts_1e-3s I.1.5.h_101pts_1e-2s |
||
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained, with a poor prediction of the asymptotic (density) solution and with a problem on the axis; conservation laws poorly satisfied. | ||||
| 10 | Convergence obtained, but for a very different asymptotic solution (for density); conservation laws not satisfied. | ||||
| I.1.5.i
D=0.1 and v=-0.3 |
3 | Convergence obtained; asymptotic solution (for density) reached. | I.1.5.i_101pts_1e-3s
I.1.5.i_51pts_1e-3s I.1.5.i_101pts_1e-2s |
||
| 4 | Convergence obtained; asymptotic solution (for density) reached. | ||||
| 7 | Convergence obtained for 1e-2s only, with a poor prediction of the asymptotic (density) solution and with a problem on the axis; conservation laws poorly satisfied. | ||||
| 10 | Convergence obtained for 1e-3s only, but for a very different asymptotic solution (for density); conservation laws not satisfied. | ||||
| I.1.5.j
D=0.1 and v=-1.0 |
3 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
I.1.5.j_101pts_1e-3s
I.1.5.j_51pts_1e-3s I.1.5.j_101pts_1e-2s |
||
| 4 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| 7 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
||||
| 10 | Failed to converge
(the number of iterations exceeds the max value of 1000). |
last update: 2012-12-13 by alves