how to discretize fourth order term

ziemowitzima · August 1, 2011, 18:27

Dear Foamers,
Does anyone of you know what is the best way to make 4 order term discretization:
I mean:
U(x,y)
U_xxxx + U_yyyy

Thanks
ZM

ziemowitzima · August 2, 2011, 17:54

so far I found such explicit solution (U == T):

volVectorField gradT=fvc::grad(T); // (T_x, T_y)
volScalarField Txxxx = gradT.component(0); // T_x
gradT = fvc::grad(Txxxx); // (T_xx, T_xy)
Txxxx = gradT.component(0); // T_xx
gradT = fvc::grad(Txxxx); // (T_xxx, T_xxy)
Txxxx = gradT.component(0); // T_xxx
gradT = fvc::grad(Txxxx); // (T_xxxx, T_xxxy)
Txxxx = gradT.component(0); // T_xxxx

Maybe someone have some better idea ?
Is it possible to descritize T_xxxx implicitly ?

-ZM

ziemowitzima · August 4, 2011, 12:26

seems to be solved:
http://www.cfd-online.com/Forums/ope...direction.html

August 1, 2011, 18:27	[solved]how to discretize fourth order term	#1
ziemowitzima Senior Member Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 145 Rep Power: 17	Dear Foamers, Does anyone of you know what is the best way to make 4 order term discretization: I mean: U(x,y) U_xxxx + U_yyyy Thanks ZM Last edited by ziemowitzima; August 4, 2011 at 12:27. Reason: solved

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August 2, 2011, 17:54		#2
ziemowitzima Senior Member Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 145 Rep Power: 17	so far I found such explicit solution (U == T): volVectorField gradT=fvc::grad(T); // (T_x, T_y) volScalarField Txxxx = gradT.component(0); // T_x gradT = fvc::grad(Txxxx); // (T_xx, T_xy) Txxxx = gradT.component(0); // T_xx gradT = fvc::grad(Txxxx); // (T_xxx, T_xxy) Txxxx = gradT.component(0); // T_xxx gradT = fvc::grad(Txxxx); // (T_xxxx, T_xxxy) Txxxx = gradT.component(0); // T_xxxx Maybe someone have some better idea ? Is it possible to descritize T_xxxx implicitly ? -ZM

August 4, 2011, 12:26		#3
ziemowitzima Senior Member Mieszko Młody Join Date: Mar 2009 Location: POLAND, USA Posts: 145 Rep Power: 17	seems to be solved: http://www.cfd-online.com/Forums/ope...direction.html