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Re: adding buoyancy forces to Biot poroelastic equations

From: Konstantinos Poulios
Subject: Re: adding buoyancy forces to Biot poroelastic equations
Date: Wed, 17 Nov 2021 08:37:07 +0100

Dear Anne-Cecile,

The GetFEM model object does not differentiate between left and right side of an equation (there is no reason for splitting equations like this), all equations are assumed to be in the form R(...)=0. So just move all terms on the same side.

The equation you provide is in strong form, you need to convert it to the respective weak form and apply the necessary integration by parts to get rid of higher order derivatives as you showed in your add_linear_term _expression_. After all these steps you should have

md.add_linear_term(mim9, 'G*Grad(u):Grad(Test_u)+G/(1-2*nu)*Div(u)*Div(Test_u)+(alpha*Grad(p)-g*(rho_tissue-rho_air*Heaviside(X(1))-rho_water*Heaviside(-X(1)))).Test_u')

you can also choose to split the term in two lines

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

md.add_linear_term(mim9, '(alpha*Grad(p)-g*(rho_tissue-rho_air*Heaviside(X(1))-rho_water*Heaviside(-X(1)))).Test_u')

but there is no reason for not keeping everything just in one term.


On Tue, Nov 16, 2021 at 11:12 PM Lesage,Anne Cecile J <> wrote:

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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