1. Grid or Mesh or Adaptive Procedure Fluid Dynamics is Made for This And this was developed in the Early 1970s

2. Fluid dynamic variables Are basically velocity and Pressure (or density) ; these vary locally in the fluid depending upon internal or external conditions. Local variations along the flow direction are best treated by the gridded approach

3. General Procedure Proper time step Advection= transport of Conserved property By fluid bulk motion

4. 2D Grid

5. 3D Cell

6. The Staggered Grid Approach What Order is this? What is the main Problem here? We don’t know the actual value of w At w_i

7. Use a staggered grid

8. 1D doesn’t have a real interpolation issue

9. Choosing the time stap You need to keep track Of the velocities to know The value of u_max

10. Advection Quantities in () Can be anything

11. The Forward Euler Integration Not real accurate but good enough for 1D Boundary Conditions become important (but not really in the 1D case(

12. The accounting problem Need to Keep Track of all the Variables (u,v,p) as A function of i,j,t

13. Finite Differences to approximate divergence + the next term involving w (for 3D)