Dear all,

Now i want to use adaptive grid in my computation to solve the N-S eqs. In adaptive grid method, the grid changes in very time step. here,i have one problem,ie., after one time step, I use the new grid, between the old and the new grid, the flow field is distributed in different physical postition. the question is: do I need interplotion between the two grids?

Thanks a lot!

Happy Xmas and New Year!

If you are using an r-refinement method, that is, you're moving the existing grid points without introducing new points, you have to either (a) interpolate the solution or (b) account for the flux generated by the moving control volume faces.

If you are using an h-refinement method and inserting new points and cells, you will need to interpolated the solution onto the new points.

Your grid is changing every time step? I assume this is a transient application?

Hi,Pete,

Thanks a lot for your help. By your illustration, I know more about the adaptive grid.

In my method. I try to solve the compressible and transient N-S eqations by compact difference scheme. I am using an r-refinement method,ie., I don't introduce new point in my method. In every time step,the grid points change in the physical computing plane. In the N-S eqations after coodinate transformation, I used the chain rule of differential calculus to expand the former terms,including the term for the time derivative. So I am not sure whether I need not interpolation or not? And could you explain your (a) and (b) solution for the question?

With Best Regards Merry Xmas and Happy New Year

Baolin Tian

You're correct in updating all the transformation metrics and Jacobians. If you account for the flux generated by the moving grid faces then that should be it, you should not need to interpolate.

As your grid moves from time step N to N+1, each face will sweep out a volume UG*A*dt, where A is the area of the face and UG is the grid velocity. You must subtract the mass/momentum/energy flux crossing the face. For example, the mass flux becomes rho*(U-UG)*A, where again UG is the grid velocity and U is the fluid velocity. Similarly for the momentum and energy flux, there is a U-UG term. If the grid does not move, the equations reduce to the usual form. Conversely, if the grid moves at the fluid velocity, there is no flux through the face.

In a steady-state simulation this would all wash out, but since you're running it transient then this has to be done.

Hope it helps.