Neumann boundary condition and Navier stokes formulation

[zonexo]

Hi,

I am now trying to simulate a flow past cylinder, imposed the NS eqns.

I wrote the current code based on the previously modified Burger's eqn code which uses ids bc.

My variables are:

x = sn.Variable('x')
y = sn.Variable('y')

u = sn.Functional('u', [x,y], 8*[80], 'tanh')
v = sn.Functional('v', [x,y], 8*[80], 'tanh')
p = sn.Functional('p', [x,y], 8*[80], 'tanh')

My qns are:

1. How do I impose the neumann bc for pressure p at the boundary?
2. In the paper, the NS eqn is given as:

L1 = u_t + p_x + lamb1 (uu_x + v*u_v ) - lamb2 ( u_xx + u_yy )
L2 = v_t + p_y + lamb1 (uv_x + vv_y ) - lamb2 *( v_xx + v_yy )

But shouldn't it be:

L1 = u_t + p_x + lamb1 (uu_x + u*u_y ) - lamb2 ( u_xx + u_yy )
L2 = v_t + p_y + lamb1 (vv_x + vv_y ) - lamb2 *( v_xx + v_yy )

(uu_x + vu_v ) -> (uu_x + uu_y )
(uv_x + vv_y ) -> (vv_x + vv_y )?

Thanks for the help!

[ssingh-ipa]

Was this issue solved? I can't find any examples where neumann boundary condition is imposed using sciann.

[pradhyumna85]

@ehsanhaghighat is it possible to implement Neumann BCs in SciANN?

[pradhyumna85]

@ssingh-ipa,
check this out: https://github.com/sciann/sciann/issues/85#issuecomment-1519419956