How to use Galerkin method to formulate finite element model for two coupled partial differential equations represent mutual interaction between structure and aerodynamics?
Can you elaborate on the problem as where exactly you facing the question? is your model compressible or in-compressible?
I'm using euler beam to represent the structural model and Theonderon theory of unsteady aerodynamics (incompressible flow) to represent the aerodynamic forces and moment...The point here is that I'm getting two coupled PDEs in which I need to apply Galarkin to formulate the mass,damping and stiffness matrices of the system...But I'm facing a problem in coupling the equations to a single finite element model....
In a simple setup let's assume that we have two dependent variables y(x,t) and z(x,t) for which you have two separate but coupled PDE's. Now can you provide if in the first pde (say y(x,t) ) you would have deferentials of z(x,t) of orders greater than zero? In other words is the coupling associated with the deferential of one another or only the functions with no deferential? The next question is if your pdes are linear or non-linear? If non-linear do you think you would consider the lineared versions?, and if still non-linear, with respect to which variables?
There are some decoupling algorithms for this issue. As i know for example in the Fluid mechanics we use velocity correction scheme or pressure correction scheme or other decoupling algorithm. Any way i think you should use the solution at the previous step to calculate unknown variable at the next step in an implicit or explicit way. Hope be useful.
Hello Hazem Saad
Decoupling is not essential for this simple system. Unfortunately, I am very busy at the moment otherwise I would give you the Galerkin discretization equations.Hope to get back to you in a few days time.
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