CVODE steps beyond the argument of stepUntil()

[rruusu]

Description

When a strongly coupled system using CVODE is used in a way that changes its input values between successive calls to stepUntil(), the changes that are made to it at that point are ignored for a period at the beginning of the next stepUntil() call.

This happens constantly, when the system takes part in a co-simulation process, in which the input values are coordinated at communication points.

[rruusu]

Here is a test case to highlight this using a very simple FMU that only contains a single integrator.

The FMU only contains Windows binaries, so there is also a Modelica file for creating it:

IntegratorTest.zip

The test case does following:

1. Creates a strongly coupled model with CVODE solver
2. Sets initial and maximum steps size to 1.0
3. Sets u to 0.0
4. Steps until 2.5 s and prints value of y
5. Sets u to 10.0
6. Steps until 5.0 s and prints value of y
7. Steps until 10.0 s and prints value of y

The expectation is that y should get a value of 25.0 at t=5.0 and 75.0 at t=10.0, but the current maintentance/v2.1 branch produces values 20.0 and 70.0.

Output from maintenance/v2.1:

info:    maximum step size for 'IntegratorTest.root': 1.000000
info:    Result file: IntegratorTest_lua.csv (bufferSize=1)
t = 0.0: y = 0
t = 2.5: y = 0
t = 5.0: y = 20
t = 10.0: y = 70
info:    Final Statistics for 'IntegratorTest.root':
         NumSteps = 15 NumRhsEvals  = 25 NumLinSolvSetups = 9
         NumNonlinSolvIters = 23 NumNonlinSolvConvFails = 0 NumErrTestFails = 4
time,IntegratorTest.root.model.integrator.y,IntegratorTest.root.model.der(integrator.y),IntegratorTest.root.model.u,IntegratorTest.root.model.y,IntegratorTest.root.model.integrator.u,IntegratorTest.root.model.integrator.initType,IntegratorTest.root.model.integrator.use_reset,IntegratorTest.root.model.integrator.use_set
0, 0, 0, 0, 0, 0, 3, 0, 0
1, 0, 0, 0, 0, 0, 3, 0, 0
2, 0, 0, 0, 0, 0, 3, 0, 0
3, 0, 0, 0, 0, 0, 3, 0, 0
2.5, 0, 0, 0, 0, 0, 3, 0, 0
4, 10, 10, 10, 10, 10, 3, 0, 0
5, 20, 10, 10, 20, 10, 3, 0, 0
5, 20, 10, 10, 20, 10, 3, 0, 0
6, 30, 10, 10, 30, 10, 3, 0, 0
7, 40, 10, 10, 40, 10, 3, 0, 0
8, 50, 10, 10, 50, 10, 3, 0, 0
9, 60, 10, 10, 60, 10, 3, 0, 0
10, 70, 10, 10, 70, 10, 3, 0, 0
10, 70, 10, 10, 70, 10, 3, 0, 0

Note that the solver also fails to actually stop at time 2.5 s, and continues to solve and emit output until 3.0 s, as it always takes a step that is the size of the maximum step size, i.e. 1.0 s in this case.

Furthermore, the model does not see the changed value for u until time 3.0 s, as seen in the integrated value at time 4.0, which should be 15 instead of 10.

We can see that strange backstep in plotting the results:

The integrator only starts to accumulate the new slope from time 3.0 s.

[rruusu]

Output from the head of #1522:

info:    maximum step size for 'IntegratorTest.root': 1.000000
info:    Result file: IntegratorTest_lua.csv (bufferSize=1)
t = 0.0: y = 0
t = 2.5: y = 0
t = 5.0: y = 20
t = 10.0: y = 70
info:    Final Statistics for 'IntegratorTest.root':
         NumSteps = 15 NumRhsEvals  = 25 NumLinSolvSetups = 9
         NumNonlinSolvIters = 23 NumNonlinSolvConvFails = 0 NumErrTestFails = 4
time,IntegratorTest.root.model.integrator.y,IntegratorTest.root.model.der(integrator.y),IntegratorTest.root.model.u,IntegratorTest.root.model.y,IntegratorTest.root.model.integrator.u,IntegratorTest.root.model.integrator.initType,IntegratorTest.root.model.integrator.use_reset,IntegratorTest.root.model.integrator.use_set
0, 0, 0, 0, 0, 0, 3, 0, 0
1, 0, 0, 0, 0, 0, 3, 0, 0
2, 0, 0, 0, 0, 0, 3, 0, 0
2.5, 0, 0, 0, 0, 0, 3, 0, 0
2.5, 0, 0, 0, 0, 0, 3, 0, 0
3, 0, 10, 10, 0, 10, 3, 0, 0
3.0001, 0.001, 10, 10, 0.001, 10, 3, 0, 0
3.0002, 0.002, 10, 10, 0.002, 10, 3, 0, 0
3.0012, 0.012, 10, 10, 0.012, 10, 3, 0, 0
3.0112, 0.112, 10, 10, 0.112, 10, 3, 0, 0
3.1112, 1.112, 10, 10, 1.112, 10, 3, 0, 0
4.1112, 11.112, 10, 10, 11.112, 10, 3, 0, 0
5, 20, 10, 10, 20, 10, 3, 0, 0
5, 20, 10, 10, 20, 10, 3, 0, 0
5.1112, 21.112, 10, 10, 21.112, 10, 3, 0, 0
6.1112, 31.112, 10, 10, 31.112, 10, 3, 0, 0
7.1112, 41.112, 10, 10, 41.112, 10, 3, 0, 0
8.1112, 51.112, 10, 10, 51.112, 10, 3, 0, 0
9.1112, 61.112, 10, 10, 61.112, 10, 3, 0, 0
10, 70, 10, 10, 70, 10, 3, 0, 0
10, 70, 10, 10, 70, 10, 3, 0, 0

Here all time steps taken by the solver are outputted, but the value at t=2.5 is an interpolation between the actual steps at t=2.0 and t=3.0.

The integrator still only starts to accumulate the new slope from t=3.0 s:

[rruusu]

That test case script could have just as well used /testsuite/resources/Modelica.Blocks.Continuous.Integrator.fmu. Such a version was added in d11ce76 to /testsuite/simulation/integratorTest.lua.

Its output now at the head of #1522:

info:    maximum step size for 'IntegratorTest.root': 1.000000
info:    Result file: integratorTest_lua.csv (bufferSize=1)
t = 0.0: y = 0
t = 2.5: y = 0
t = 5.0: y = 25
t = 10.0: y = 75
info:    Final Statistics for 'IntegratorTest.root':
         NumSteps = 16 NumRhsEvals  = 26 NumLinSolvSetups = 13
         NumNonlinSolvIters = 24 NumNonlinSolvConvFails = 0 NumErrTestFails = 4
time,IntegratorTest.root.integrator._D_outputAlias_y,IntegratorTest.root.integrator.der(_D_outputAlias_y),IntegratorTest.root.integrator.local_set,IntegratorTest.root.integrator.u,IntegratorTest.root.integrator.y,IntegratorTest.root.integrator.initType,IntegratorTest.root.integrator.local_reset,IntegratorTest.root.integrator.use_reset,IntegratorTest.root.integrator.use_set
0, 0, 0, 0, 0, 0, 3, 0, 0, 0
1, 0, 0, 0, 0, 0, 3, 0, 0, 0
2, 0, 0, 0, 0, 0, 3, 0, 0, 0
2.5, 0, 0, 0, 0, 0, 3, 0, 0, 0
2.5, 0, 0, 0, 0, 0, 3, 0, 0, 0
2.5001, 0.001, 10, 0, 10, 0.001, 3, 0, 0, 0
2.5002, 0.002, 10, 0, 10, 0.002, 3, 0, 0, 0
2.5012, 0.012, 10, 0, 10, 0.012, 3, 0, 0, 0
2.5112, 0.112, 10, 0, 10, 0.112, 3, 0, 0, 0
2.6112, 1.112, 10, 0, 10, 1.112, 3, 0, 0, 0
3.6112, 11.112, 10, 0, 10, 11.112, 3, 0, 0, 0
4.6112, 21.112, 10, 0, 10, 21.112, 3, 0, 0, 0
5, 25, 10, 0, 10, 25, 3, 0, 0, 0
5, 25, 10, 0, 10, 25, 3, 0, 0, 0
6, 35, 10, 0, 10, 35, 3, 0, 0, 0
7, 45, 10, 0, 10, 45, 3, 0, 0, 0
8, 55, 10, 0, 10, 55, 3, 0, 0, 0
9, 65, 10, 0, 10, 65, 3, 0, 0, 0
10, 75, 10, 0, 10, 75, 3, 0, 0, 0
10, 75, 10, 0, 10, 75, 3, 0, 0, 0

Plot of the result: