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Old   August 11, 2008, 14:55
Default Immersed Boundary Formulation
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Hi, I am writing my own code and I want to use immersed boundary method for simulating flow around moving bodies. I have a question regarding the formulation.

According to formulation of Mohd.Yusof we have


where n is the time advanceme and (i,j) are the x and y co-ordinates

If the boudnary is conciding with a grid point and has velocity V we have

-->f(n)=V-u(n)/dt-Rhs(n). --> u(n+1)=u(n)+Rhs(n)*dt+f(n)*dt --> u(n+1)=u(n)+Rhs(n)+((V-u(n)/dt)-Rhs(n))*dt --> u(n+1)=V

If stationary and no -slip is used V=0 --> u(n+1)=0

am I correct to this point??

If the immersed point is not coinciding with the grid point use linear interpolation and instead of V we have velocity at a particular point for example at u(n)(i,j) to be u(n)(i,j+1)*fac (where the fac is the factor used to multiply that can be computed using linear interpolation so that zero falls in between them)i.e.


using same procedure as above we have

--> u(n+1)(i,j)=fac*u(n)(i,j+1)

am I correct here ???

Is my formulation ok?? Thanks in advance

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