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Fluid Dynamics Simulation: Momentum Balance and Continuity Equation Analysis

Explore momentum balance and continuity equations in fluid dynamics simulation. Analyze water level slopes in u and v points. Follow a step-by-step procedure for computational analysis in the local grid direction.

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Fluid Dynamics Simulation: Momentum Balance and Continuity Equation Analysis

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  1. o c v + u z

  2. dsu(i,j) o + i,j

  3. dsz(i,j) o + i,j

  4. dsv(i,j) o + i,j

  5. dsc(i,j) o + i,j

  6. dnu(i,j) o + i,j

  7. dnz(i,j) o + i,j

  8. dnv(i,j) o + i,j

  9. dnc(i,j) o + i,j

  10. dsdnu(i,j) o +

  11. Momentum balance in u direction • Only consider advection of velocity component in the local grid direction

  12. Continuity equation • Multiply continuity equation with u

  13. Subtract continuity eq. times u from momentum equation and divide by V

  14. Procedure • Go around the cell centered at u-point • Compute q across cell boundary by averaging qx resp. qy • If q is inward • Compute Qin by multiplying with dnzrespdsc • Compute uin as • Add Qin (uin–u) to advection

  15. dsdnz(i,j) +

  16. dsdnv(i,j) +

  17. Water level slopes in u, v points

  18. Continuity

  19. Wave propagation

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