adding buoyancy forces to Biot poroelastic equations

[Lesage,Anne Cecile J]

Dear all

 

To implement the building of my fem matrix for the mechanical equilibrium, I presently write

md.add_linear_term(mim9, 'G*Grad(u):Grad(Test_u)+G/(1-2*nu)*Div(u)*Div(Test_u)+alpha*Grad(p).Test_u')

 

How can i add an additional buoyancy terms to the equation (see right-hand side attached equation picture)?

gravity is vector g = - 9180 N along the x axis for my mesh

rhot (density tissue is constant) but rhof = rho water for x<0 and rhof = rho air for x>0

 

Thank you

Anne-Cecile Lesage

 

 

 

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mechanicaleqbuoyancy.png
Description: mechanicaleqbuoyancy.png