###### Q2. What is the VOF function used to track the free surface of a cell?

To track the free surface the VOF function Fs is used, which is 0 if no fluid is present in the cell, 1 if the open part of the cell is completely filled with fluid and between 0 and 1 if the cell is partly filled with fluid.

###### Q3. What grids have been used to investigate the convergence of the method?

To investigate convergence of the method under grid refinement, the circular cylinder entry simulations have also been run with different grids.

###### Q4. What is the stability of the equation for uncut cells?

In the case of uncut cells with fixed objects the stability of the equation containing the time integration term and the convective term is given by the CFL-restriction, which in one dimension reads dtjuj/h 6 1 (h is the size of the uncut cell).

###### Q5. What is the first series of simulations?

The second series of simulations consists of drop tests, where wedges with different dead-rise angles, a circular cylinder and a cone are entering the water.

###### Q6. What is the condition used to prevent the waves from reflecting from the boundary?

when performing wave simulations an inflow boundary is needed where the incoming wave is prescribed, and at the opposite boundary a non-reflecting outflow condition should be used.

###### Q7. What is the discrete gradient operator in the pressure term?

Using this discretisation, the discrete gradient operator in the pressure term is the negative transpose of the discrete divergence operator Eq. (9), which is also an analytic property ($ = ($Æ)T) [43].

###### Q8. What is the condition needed to prevent the waves from reflecting from the boundary?

At the outflow boundary a non-reflecting boundary condition is needed to prevent the waves from reflecting from the boundary into the domain.

###### Q9. What is the weight factor used for when the body is moving?

The weight factor K has been chosen such that the stabilising term is only used when the body is moving; note that it equals unity for fixed objects.

###### Q10. What is the boundary condition that defines the pressure at the free surface?

The boundary condition that defines the pressure at the free surface is given by Eq. (5), which describes the continuity of normal stresses.

###### Q11. How can the hydrodynamic force of a circular cylinder be estimated?

For the initial state of the entry of a circular cylinder, the hydrodynamic slamming force can be estimated byF ¼ V q p 2 ð2VR 2V 2tÞ; ð46Þwhere t denotes time with t = 0 the moment of first impact.

###### Q12. What is the VOF method used to assess the performance of the fluid-displacement?

To assess the performance of the displacement method, the standard advection test of rotation of a slotted disk, defined by Zalesak [46], has been performed.

###### Q13. What is the stability criterion for cut cells?

The X in this estimation cancels the contribution of X 1 in X 1C, leaving the stability criterion for cut cells the same as for uncut cells [10].

###### Q14. What is the integrand in two dimensions?

In two dimensions the integrand can be written as the sum of the second order horizontal and verticalderivatives of the horizontal velocity.

###### Q15. What is the current method for calculating the motion of the body?

In the current method the objects are either moving with a prescribed motion, or the motion is calculated from the interaction between the object and the liquid dynamics.

###### Q16. What is the slamming coefficient of a circular cylinder?

The slamming coefficient is given by Cs = F/qRV2, with F the total vertical hydrodynamic force, R the radius of the circular cylinder and V the entry velocity.

###### Q17. What is the direction of the function that is normal to the free surface?

The direction in which the function is defined is the direction of the coordinate axis that is most normal to the free surface (which is the positive z-direction in Fig. 5).