A second-order changing-connectivity ALE scheme and its application to FSI with large convection of fluids and near contact of structures

We propose a second-order characteristic-inclined changing-connectivity arbitrary Lagrangian–Eulerian (ALE) scheme. It does not explicitly calculate the characteristics but allows characteristic-inclined discretization. Large mesh distortions are prevented by mesh smoothing and edge/face swapping techniques. The resulting semi-implicit scheme can therefore handle problems with large deformation of the domain and strong convection of the fluid. The fact that we only need to solve a linear system of equations for a near symmetric matrix in each time step makes the scheme very appealing. We use the standard Pm/Pm−1Pm/Pm−1 (m≥2m≥2) or P1-bubble/P1P1-bubble/P1 (m=1m=1) finite elements and prove that the scheme converges at rate O(Δt2+hm+2Δt+hm+1) in the incompressible Navier–Stokes equations (NSE) case. This gives optimal convergence rate when h/Δt=O(1)h/Δt=O(1). To prove this result, we introduce a new interpolation operator which is easy to implement and enables us to keep the optimal convergence rate even if we change the connectivity of the mesh in every time step. Numerical tests also confirm our theoretical results. We then apply our ALE scheme to solve fluid structure interaction (FSI) problems which may contain large convection of fluids and near contact of structures. We prove the stability of the fully discrete semi-implicit second order FSI scheme. We then numerically confirm the order of convergence using a recently proposed 2D manufactured solution for FSI. In this example, part of the fluid domain can become arbitrarily narrow before going back to normal. Numerical tests for flow around rotating rigid and elastic crosses and flow induced opening and near-closing of a heart valve are performed.