h=1 h=0 At an internal node vol. Balance gives vel of volume sides And continuity gives hence i.e., At each point in time we solve A steady state problem in current Domain. Deforming 2-D grid for Filling Problem—3D version a project?

On moving boundary in bo =0 from boundary condition and Can use this to update node position on boundary

xx yy i (h i =0) (in direction Of average normal To surfaces that meet at p --exact direction not critical) And with the setting Then splitting boundary into 2 segments

xx yy i So for a given nodal h filed the equation provides an explicit means of finding the A and y displacements at node I that will recover the volume balance NOTE end points on boundary are constrained to move in x-direction or y-direction. At End point 1 set c= and at End point2 set c=

Steps in Solution for Filling problem 1.Set up grid assuming a small initial radius r = 1.1 say, set  say  2. Calculate and store coefficients 3. Set up boundaries 4. solve steady state problem Fixed =1 NO Fixed =0 NO 5. Calculate update boundary displacements In a time step iterations of the following 6. Calculate x- displacements globally through solving Use Current Coefficients with boundary settings Fixed =  x i NO Fixed =  7. Do same for y-displacements 8. Update node point locations (under relax) 9. Repeat to end of iterations 10. At end of time step calcs Set 11. Go to next time step