[selig5576]

For the nonlinear advection term, I am handling it with the QUICK scheme. Something I am curious about is for the ghost nodes, will using a 1st order method (say upwind) be sufficient? I am using first order upwinds at i=2, i=nx-1, j=2, j=ny-1 (the nodes that are not accounted for in my stencil), but having running into a problem where I get a slight oscillation after a few time steps at the inlet BC. For the sake of debugging, I disabled the advection term and the problem goes away, so I'm sure its a bug in how I am handling the inlet ghost node. As such, is using first order methods subject to injecting oscillations in my numerical solution?

The picture I provided illustrates the oscillation at the bottom of the jet formation. I am working with a moderate Reynolds number of 1000 and a grid of 100 x 100. Even if I increase my resolution to 300 x 300 I still get the oscillation.

[FMDenaro]

Using a first order approximation just lower the accuracy order, cannot produce oscillations...I think about some bugs..
However, think about the fact that you need to prescribe directly the flux on the boundary and this way no ghost points would be involved.

Try to chek the solution only after the first time step to see if you have problem at the inflow

[selig5576]

You are right in that I can adjust the flux at the boundary and don't need to solve the equation at the boundaries.

wind direction > 0

CxM(2,j) = (1.0/dx)*(u(2,j)*max(u(2,j),0.0) - u(1,j)*max(u(1,j),0.0)) + (1.0/dy)*(max(u(2,j),0.0)*v(2,j) - max(u(2,j-1),0.0)*v(2,j-1))
CyM(2,j) = (1.0/dx)*(u(2,j)*max(v(2,j),0.0) - u(1,j)*max(v(1,j),0.0)) + (1.0/dy)*(v(2,j)*max(v(2,j),0.0) - v(2,j-1)*max(v(2,j-1),0.0))

wind direction < 0

CxP(2,j) = (1.0/dx)*(min(u(3,j),0.0)*u(3,j) - min(u(2,j),0.0)*u(2,j)) + (1.0/dy)*(min(u(2,j+1),0.0)*v(2,j+1) - min(u(2,j),0.0)*v(2,j))
CyP(2,j) = (1.0/dx)*(u(3,j)*min(v(3,j),0.0) - u(2,j)*min(v(2,j),0.0)) + (1.0/dy)*(min(v(2,j+1),0.0)*v(2,j+1) - min(v(2,j),0.0)*v(2,j))

Essentially for the u-momentum, specfically uv_y I min/max the v velocity and for the v-momentum, uv_x, I min/max the u velocity. I am just ensuring that I did not miss something. I am focussing on this as this computation is influenced by the inlet BC.

EDIT: after 1 time step, I do not see the instability.

[selig5576]

To whom it may concern. My problem was due to the fact that I was checking the direction of the wrong velocity term. It is all fixed now