Simulation of 2D fluid–structure interaction in inviscid compressible flows using a cell-vertex central difference finite volume method

Abstract

In the present study, the applicability and accuracy of a cell-vertex finite volume method developed are assessed in simulating 2D fluid–structure interaction in inviscid compressible flows where the nonlinear phenomena exist in both the unsteady transonic fluid flows and the large nonlinear deformation of solid structures. The unsteady Euler equations are considered as the governing equations of the fluid flow in the arbitrary Lagrangian–Eulerian form and the large nonlinear deformation of the solid structure is considered to be governed by the Cauchy equations in the total Lagrangian form. Both the domains are discretized by a second-order central-difference cell-vertex finite volume method in space on arbitrary quadrilateral grids and a second-order implicit method in time. For each time step, the resulting set of coupled implicit nonlinear equations in either domains is solved iteratively in the pseudo-time. The fluidic and structural parts are coupled in a partitioned manner for the simulation of fluid–structure interaction problems where at the interface the grids of the two domains are coincident. The formulation for the structural dynamics applied here can accurately simulate different types of boundary conditions. It can also properly model the panel thickness and therefore the stress distribution within the structure can be reasonably obtained. Some benchmark test cases are studied and the results obtained are compared with the available experimental/numerical results. Simplicity of the implementation, similarity of the discretization and accuracy of the solution demonstrate the capability and robustness of the solution methodology proposed in simulating fluid–structure interaction problems in compressible flows.