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We present a structure preserving discretization of the fundamental spacetimegeometric structures of fluid mechanics in the Lagrangian description in 2D and3D. Based on this, multisymplectic variational integrators are developed forbarotropic and incompressible fluid models, which satisfy a discrete version ofNoether theorem. We show how the geometric integrator can handle regular fluidmotion in vacuum with free boundaries and constraints such as the impactagainst an obstacle of a fluid flowing on a surface. Our approach is applicableto a wide range of models including the Boussinesq and shallow water models, byappropriate choice of the Lagrangian.

Multisymplectic variational integrators for barotropic and incompressible fluid models with constraints