:
This paper presents a simplified formulation of 2D solid-fluid interactions using the concept of Shis manifold method, which separates mathematical mesh from physical mesh. Solid blocks are formulated mainly according to Shis discontinuous deformation analysis. The mathematical mesh for the fluid domain is fixed three-noded finite elements, and its physical domain is delimited by the outer boundaries of blocks and other impervious boundaries. Along the block-fluid interfaces, fluid applies traction on the solid outer boundaries, which instead serve as impervious barriers to fluid. Accordingly, the formulation does not produce the coupled sub-matrix terms such as [K]BF and [K]FB, and the global equations can be solved separately for solids and fluid, avoiding the difficulty in solving unknowns with incompatible dimensions.
Since the manifold method was first introduced by Shi (1992), the concept and potential use of this method has drawn great attention from international researchers in both the mathematical and engineering fields. This method is potentially useful for solving complex material problems such as composite materials, fracture propagation, multi-phase flows, etc. By separating mathematical and physical meshes, the manifold method can handle problems involving complex and different material domains. The mathematical mesh does not only relate to the physical behavior of a material, but also includes the numerical discretization scheme in space as well as the shape function used. Selection of mathematical meshes may be quiet arbitrary, and possible ones are finite element, finite difference, polynomial or element-free (BeIytschko etc., 1994) meshes. The physical mesh represents the complex space occupied by a material, and thus equals to the integration domain in a numerical analysis. The physical mesh is given and cannot be changed arbitrarily. Additionally with the "finite cover" concept, the manifold method can model a wide variety of continuous or discontinuous materials. The early applications of the manifold method (Shi 1992, Lin 1995, Lin & Mo 1995, Wang etc. 1995, Ke 1995a) are mainly focused on the solid material world. This paper provides a first attempt to formulate 2D solid-fluid interactions using the concept of Shi's manifold method. The system unknowns are the block displacements and fluid quantities.
The solid blocks are formulated mainly based on the discontinuous deformation analysis, DDA (Shi 1988). DDA adopts displacements as unknowns which are solved implicitly, fully satisfies dynamic equilibrium, and has complete block kinematics for block contacts.
The mathematical mesh for the fluid domain is fixed three-noded finite elements, and its physical domain of fluid is defined by the outer boundaries of solid blocks and other impervious boundaries. The free surface boundaries of fluid are not considered in the current stage of this study. Figure 1 shows the partial finite element mesh (dashed lines) of a fluid domain, with the bottom part in contact with a solid block. The integration area of each fluid element in contact with solid blocks may be irregular, e.g. Polygon P1P3P15P1Pd as shown in Figure 1.
