Giovanni Russo Abstract. The Hamiltonian formulation of incompressible, inviscid fluid dynamics is recalled. Numerical methods based on this formulation have several conservation properties that make them attractive. This formulation is applied to study the interaction of a fluid with a membrane in two and three dimensions.
Linear analysis is performed in two and three dimensions for axisymmetric flow.
The result in two dimensions agrees with linear analysis obtained by the vorticity formulation. Numerical schemes based on this formulation are derived and applied to the evolution of membranes in two and three dimensions. The numerical results are in agreement with linear analysis. Hamiltonian formulation, incompressible inviscid fluids, numerical methods for PDEs AMS Subject Classifications . 70H, 76C, 65M PII .