Mathematical modeling of fluid flows for underwater missile launch

The gas and water flows during an underwater missile launch are numerically studied. For the gas flow, the explicit difference scheme of Non-oscillation and Non-free-parameter Dissipation (NND) is utilized to solve the Euler equations for compressible fluids in the body-fitted coordinates. For the water flow, the Hess-Smith method is employed to solve the Laplace equation for the velocity potential of irrotational water flows based on the potential theory and boundary element method. The hybrid Eulerian-Lagrangian formulation for the free boundary conditions is used to compute the changes of the free surface of the exhausted gas bubble in time stepping. On the free surface of the exhausted gas bubble, the matched conditions of both normal velocities and pressures are satisfied. From the numerical simulation, it is found that the exhausted gas bubble grows more rapidly in the axial direction than in the radial direction and the bubble will shrink at its ‘neck’ finally.