An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems

Abstract

The free surface capturing method based on Cartesian cut cell mesh is extended to the water-entry and -exit fields with body-fluid interaction. The governing equations are the incompressible Euler equations for a variable density fluid system with a free surface, which is treated as a contact discontinuity. The solver is based on the artificial compressibility method with a dual time-stepping technique for time advancing and the finite-volume method with a high-resolution Godunov-type upwind scheme on spatial discretization. For solving the numerical problem caused by the extension, the acceleration term of body is introduced for the new pressure condition of moving solid boundary, and the exact Riemann solution is used to calculate the flux of the solid boundary. In addition, a new solution of gradients based on the least-squares idea is presented for simply calculating the gradients. Finally, test cases show that the present method is available and can be successfully applied in various water-entry and -exit phenomena.

Comments on ‘An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems’

“…The contradictory results reported in Wang & Wang (2009) may indicate errors from other sources unrelated to the acceleration term in the pressure boundary condition.…”

“…Further to this and as an attempt to improve the numerical stability of their code, the exact solution of a Riemann problem for moving boundaries has been used for calculating the fluxes at the boundary (Causon et al 2001). According to the authors (Wang & Wang 2009), the main reason for the inclusion of the acceleration term in the pressure boundary condition was that without this term their method would substantially under-predict the impact forces and even diverge at some point in the numerical simulation. Although it is well known that the acceleration term can be important for some flow problems where the solid boundary undergoes rapid change in velocity, it can be demonstrated that for the wedge water-entry problem as described in the experimental and theoretical work of Zhao et al 1997, this term will not have much effect on the simulation results.…”

“…Subsequently, the method has been specifically extended and applied to waterentry problems by Wang & Wang 2009, in which several improvements to the original method were claimed by the authors, including, most notably, the implementation of a new pressure boundary condition at moving solid surfaces. The unsteady term owing to the acceleration of solid bodies in the momentum equations was retained when calculating the pressure gradient at the surface of a solid boundary.…”

“…The wedge is 0.5 m wide and has a mass of 241 kg. The computational domain of 2 m × 2 m is divided into 200 × 200 uniformly square mesh cells of the size 0.01 m × 0.01 m, which is the same as used by Wang & Wang (2009). In the simulation, the densities for water and air are taken as 1000 and 1 kg m −3 , respectively, and the value for the artificial compressibility parameter b is taken as 1000.…”

Further Application of Surface Capturing Method and Cartesian Cut Cell Mesh on Hydroelastic Water-Entry Problems of Free-Falling Elastic Wedge

“…Thus in order to better predict the force and motion of body and achieve fluid information near free surface simultaneously, a CFD method should be applied in water entry problem. Furthermore, compared with the traditional CFD method ( [36,[42][43][44] and so on), the surface capturing method [45][46][47][48] based on Cartesian cut cell mesh [47][48][49][50][51][52] as a novel method can not only well simulate complicated cases of wave breaking and trapping, but also has higher computational efficiency to treat moving boundaries by updating a few cut cells locally rather than remeshing the whole flow domain. On the other hand, so far there are only few documents which consider the interaction among fluid field, global motion, and local deformation of elastic body simultaneously for the water entry problem.…”