A numerical algorithm for hydrodynamic free boundary problems

A generalized formulation of inviscid incompressible hydrodynamics as a system of conservation laws subject to a one-sided density constraint is used as the basis of a numerical algorithm for a variety of hydrodynamic free surface problems. Benchmark calculations for colliding masses of fluid and for the motion of a spherically symmetric bubble are compared with theoretical predictions. Also shown are profiles calculated for an evolving underwater bubble near a wall. Energy dissipation is introduced as a measure of turbulence and is used in analyzing the numerical results. Convergence behavior of the numerical algorithm is discussed.

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