Fluid-structure interaction system predicting both internal pore pressure and outside hydrodynamic pressure

In this paper, we present a numerical model for fluid-structure interaction between structure built of porous media and acoustic fluid, which provides both pore pressure inside porous media and hydrodynamic pressures and hydrodynamic forces exerted on the upstream face of the structure in an unified manner and simplifies fluid-structure interaction problems. The first original feature of the proposed model concerns the structure built of saturated porous medium whose response is obtained with coupled discrete beam lattice model, which is based on Voronoi cell representation with cohesive links as linear elastic Timoshenko beam finite elements. The motion of the pore fluid is governed by Darcy's law, and the coupling between the solid phase and the pore fluid is introduced in the model through Biot's porous media theory. The pore pressure field is discretized with CST (Constant Strain Triangle) finite elements, which coincide with Delaunay triangles. By exploiting Hammer quadrature rule for numerical integration on CST elements, and duality property between Voronoi diagram and Delaunay triangulation, the numerical implementation of the coupling results with an additional pore pressure degree of freedom placed at each node of a Timoshenko beam finite element. The second original point of the model concerns the motion of the outside fluid which is modeled with mixed displacement/pressure based formulation. The chosen finite element representations of the structure response and the outside fluid motion ensures for the structure and fluid finite elements to be connected directly at the common nodes at the fluid-structure interface, because they share both the displacement and the pressure degrees of freedom. Numerical simulations presented in this paper show an excellent agreement between the numerically obtained results and the analytical solutions.