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How to code Strang splitting ?

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Old   January 11, 2020, 13:41
Default How to code Strang splitting ?
  #1
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Best wishes to all in this new year


I couldn't find how to do this in openFoam and all of its variants.

Strang splitting means

df/dt = T + S

becomes

df/dt = S
df/dt = T
df/dt = S

T stands for convective and diffusive terms whereas S stands for a source term. Also the original dt for the derivative numerical scheme is halved for both df/dt = S in the above



I think what should be done for two fields f1 and f2 is as follows. (S1 and S2 may depend non linearly on both f1 and f2)


....


delT = runTime.deltaT().value();


runTime.deltaT().value() = delT/2.;


solve
(
fvm::ddt(f1) == T1
) ;


solve
(
fvm::ddt(f2) == T2
) ;


runTime.deltaT().value() = delT;


solve
(
fvm::ddt(f1) == S1
) ;


solve
(
fvm::ddt(f2) == S2
) ;



runTime.deltaT().value() = delT/2;


solve
(
fvm::ddt(f1) == T1
) ;


solve
(
fvm::ddt(f2) == T2
) ;


runTime.deltaT().value() = delT;

....

Is anything wrong with my approach ? Any reply welcome
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Old   January 13, 2020, 14:28
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Well, Im going to give you a first clue


you cannot set it this way

doubleScalar delT = runTime.deltaT().value();

runTime.deltaT().value() = delt/2;

I checked using Info that the original value isnt changed.

Instead, you have to write

runTime.setDeltaT
(
delT/2.
);


I will keep you posted after I study more about these time objects
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Old   March 26, 2020, 12:48
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alexander thierfelder
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Hey I found out that it should be possible with subCycle. But I don't know how to implement that the right way

"Strang splitting is an
alternative to this method, in which the sweeps are performed in a symmetric order. An odd
number of sweeps are required for this splitting, i.e. M = 3, 5, 7.., and the reaction terms are
always integrated explicitly at the middle iteration (M + 1)/2. The homogeneous terms are
integrated implicitly. The example is given for M = 3: The sub-cycling is implemented using the built-in subCycle utility. This functionality alters
the current time index of the corresponding volume field, assuring that sub-iterations are
stored as t+i/N and the final iteration corresponds to the current time step t+1, instead of
t+N which would be the case of the time indices are not corrected."

Source:
https://repository.tudelft.nl/island...m/OBJ/download
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Old   May 24, 2020, 08:46
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alexander thierfelder
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For the simplest case n =3 ,I think it should work somehow like this:
Code:
label nSubCycles = 3;
dimensionedScalar totalDeltaT = runTime.deltaT();
                
 for ( subCycle<volScalarField> YSubCycle(Y, nSubCycles); !(YSubCycle).end(); ++YSubCycle)
{

     if ( YsubCycle.index() != 2 )
     { 
        runTime.setDeltaT(totalDeltaT/2);
        #include "YEqnHom.H"
        YEqnHom.solve();
     }
     else 
     {
         runTime.setDeltaT(totalDeltaT);
         #include "YEqnHet.H"
         YEqnHet.solve();
     }
}
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Old   June 6, 2020, 07:25
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alexander thierfelder
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And for any number of sub cycles (odd).

Code:
label nSubCycles = 5; // odd

dimensionedScalar totalDeltaT = runTime.deltaT();
                
 for ( subCycle<volScalarField> YSubCycle(Y, nSubCycles); !(YSubCycle).end(); ++YSubCycle)
{

     if ( YsubCycle.index() != (floor(nSubcycle/2)+1) )
     { 
        runTime.setDeltaT(totalDeltaT/(nSubcycle-1));
        #include "YEqnHom.H"
        YEqnHom.solve();
     }
     else 
     {
         runTime.setDeltaT(totalDeltaT);
         #include "YEqnHet.H"
         YEqnHet.solve();
     }
}

Last edited by superkelle; June 6, 2020 at 15:23.
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