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VARIABLEDT

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User's manual

To activate a variable time step bounded between a minimum and maximum DT, in configuration file Model_x.dat

VARIABLEDT  : 1
DT          : 10.
MAXDT       : 100.

A log file DTLog.txt is stored in the results folder /res of the main domain if the option DT_LOG is set in the nomfich.dat file in /exe folder of the main domain. Such a log file is useful to trace which cell of which property is the weakest link that could generate an instability.

DT_LOG                    : ..\res\DT_Log_2.log

An option can be checked in MOHID Studio or MOHID GUI that enables the logging of variable time steps.

An excerpt of a log file looks like this (Iterartion number, dt, i, j, k, model name, property name):

      1, DT:    10.000, I:  177, J:   75, K:   43, Model - Property: Portugal - momentum
      2, DT:    10.000, I:   37, J:    1, K:   43, Model - Property: Portugal - momentum
      3, DT:    10.000, I:  177, J:  101, K:   43, Model - Property: Portugal - momentum
      4, DT:    10.000, I:   62, J:    1, K:   43, Model - Property: Portugal - momentum
      5, DT:    10.000, I:  156, J:   93, K:   25, Model - Property: Portugal - nitrate
      6, DT:    10.000, I:   69, J:    1, K:   43, Model - Property: Portugal - momentum
      7, DT:    10.000, I:  177, J:   84, K:   43, Model - Property: Portugal - momentum
      8, DT:    10.000, I:   64, J:    1, K:   43, Model - Property: Portugal - momentum
      9, DT:    12.000, I:  155, J:  106, K:   33, Model - Property: Portugal - nitrate
     10, DT:    13.846, I:   65, J:    1, K:   49, Model - Property: Portugal - nitrate
     11, DT:    16.364, I:   25, J:    4, K:   45, Model - Property: Portugal - nitrate
     12, DT:    18.000, I:   32, J:    6, K:   43, Model - Property: Portugal - nitrate
     13, DT:    20.000, I:   26, J:    6, K:   44, Model - Property: Portugal - nitrate
     14, DT:    22.500, I:   27, J:    8, K:   44, Model - Property: Portugal - nitrate
     15, DT:    25.714, I:  156, J:  119, K:   30, Model - Property: Portugal - nitrate
     16, DT:    30.000, I:   32, J:    4, K:   42, Model - Property: Portugal - silicate acid
     17, DT:    36.000, I:   30, J:    3, K:   42, Model - Property: Portugal - silicate acid
     18, DT:    36.000, I:   27, J:   10, K:   44, Model - Property: Portugal - nitrate
     19, DT:    36.000, I:   32, J:    6, K:   43, Model - Property: Portugal - silicate acid
     20, DT:    36.000, I:   30, J:    5, K:   42, Model - Property: Portugal - silicate acid

Physical rationale

The main idea to compute an ideal time-step is to choose the largest time-step above which the numerical model iteration would overshoot. This is equivalent to making sure that no cell in any property can deplete more than its property mass in one time-step, given that it has a net flux with positive divergence. Mathematically speaking this would be equivalent to:

Failed to parse (unknown error): \Delta t = \min_{p\;ijk} \left( \frac{ m }{ \Phi } \right) \quad\;\;\;\; \text{if}\quad\;\;\Phi \gt 0 .

where m and \Phi are, respectively, the mass (kg\,m^{-3}) and the net massic flow (kg\,m^{-3}\,s^{-1}) of the property p at the cell indexed by i,\,j,\,k.

This takes into account only advective and diffusive fluxes but disregards sources and sink terms. For momentum, it also disregards the time-step constraints imposed by the gravity surface wave mode or any other physical process occuring at scales below ten times the computed  \Delta t .

See also