computing lift drag coeff in immersed boundary mtd

zonexo

hi,

i would like to know how ppl usually compute the lift,drag coefficient for an 2D arbitrary body in the flow in an immersed boundary (IB) mtd. discretization is done using FVM

i've done it by :

1. pressure on each cut surface of the IB is obtained by extrapolating along the normal using polynomial ie p=a0 + a1*n + a2*n^2. since dp/dn=0, p=a0+a2*n^2 where n=0 at surface. p at 2 other pts along the normal is obtained by linear or bilinear interpolation. pressure normal force is then p*(cut surface length)

2. objective is to get du(t)/dn & du(n)/dn which n=normal,t=tangential of surface. similarly, u(t,n)=a0 + a1*n+ a2*n^2. so du(t,n)/dn=a1 + 2*a2*n. as b4, u(t,n) along normal is obtained using linear/bilinear interpolation and resolved in the n/t direction.

3. shear force=(cut length)*du(t)/dn/Re. normal=(cut length)*2*(du(n)/dn/Re (non-dimensional)

4. all the forces are summed up and resolved back in the horizontal/vertical direction.

can someone comment on the mtd? i find that it's accurate if a symmetrical body is cut equally by the grid. however if the grid is not cut equally, errors will appear such as non zero lift when it should be zero.

I'm sure my way of computing is not the best.I hope some ppl can suggest better mtds or give references. Tks!