An embedded boundary method for the Navier-Stokes equations on a time-dependent domain (Q444535)

The authors present a new conservative Godunov-projection method on Cartesian grids for numerical solution of the Navier-Stokes equations in moving domains. The method uses the unique Hodge decomposition of a vector to determine the divergence-free component and the pressure gradient. In this method the hyperbolic advection and corresonding (explicit or implicit) Helmhotz operations are performed on time-stationary domains. Moving boundary is approximated by the embedded boundary method with cut-cell stability through hybridization. More precisely, the domain boundary is modelled as the zero of a distance function level set. All geometric descriptions are derived at the moving front from the discrete level set. In this paper boundary motion is explicitly given. In order to transfer data from one fixed domain to another one a third order interpolation is applied. The authors show that the resulting method is second order accurate in \(L_1\) and first order accurate in \(L_\infty\) on a numerical experiment with flow past a shrinking sphere.