Interface stabilised finite element method for moving domains and free surface flows

A recently developed stabilised finite element method which draws upon features of both continuous and discontinuous finite element methods is generalised for the incompressible Navier–Stokes equations on moving domains and for free surface problems. The approach allows the natural incorporation of upwinding of the advective flux, and the formulation is stable when using equal-order Lagrange basis functions for the velocity and pressure fields. Particular attention is paid to the formulation of a fractional step algorithm for moving domain problems. Numerous applications to environmental free surface flows are presented, ranging from simple test cases to simulations of sophisticated laboratory experiments. It is shown that the formulation, which contains no flow-dependent stabilisation parameters, is able to model a wide range of flow conditions stably without user intervention, and it is shown that negligible numerical dissipation is introduced. The physics of the considered numerical examples involves sensitive free surface wave behaviour, which has been accurately captured due to the stability of the model together with negligible introduced numerical dissipation.