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**An improved free surface capturing method based on Cartesian cut cell mesh for water-entry and -exit problems.**
*(English)*
Zbl 1186.76666

Summary: 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.

### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

### Keywords:

free surface capturing method; Cartesian cut cell mesh; body-fluid interaction; acceleration term; exact Riemann solution; least-squares idea
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\textit{W. Wang} and \textit{Y. Wang}, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2106, 1843--1868 (2009; Zbl 1186.76666)

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