A finite element method based on level set and combined formulation was studied for the analysis of entry problem of an elastic body. Both free surface tracking and the interaction of an entry body with the fluid flow need to be considered in the entry problem. Free surface tracking was achieved using a level set method in which advection and reinitialization equations for level set variable were discretized using a least square finite element method. The coupling of the motion of the elastic body with fluid flow was conducted using combined mixed finite element formulation. ALE (arbitrary Lagrangian Eulerian) method was adopted for the movement of a grid since the downward motion of the body is dominant in entry problem. Since a mixed finite element is adopted, a linear basis function that belongs to H1 space is used for velocity and level set variables on each sub-element (Th) while a linearly interpolated pressure variable that belongs to L2 space is adopted on each element (T2h). The level set method based on a least square finite element method was verified by solving some free surface tracking problems and then, the finite element formulation for entry problem was validated by comparing with an existing experimental results. Further, the comparison of the entry of an elastic body with that of a rigid body was investigated.

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