An arbitrary Lagrangian–Eulerian gradient smoothing method (GSM/ALE) for interaction of fluid and a moving rigid body

Abstract

The gradient smoothing method (GSM) was recently proposed for fluid dynamic problems governed by the Navier–Stokes equations, using unstructured triangular cells. This work extends the GSM to solve the fluid–rigid body interaction problems, by combining the GSM with the arbitrary Lagrangian–Eulerian (ALE) method to handle moving solid in fluids. A moving mesh source term derived directly from the geometric conservation law is incorporated into the discrete equations to ensure the recovery of uniform flow while the mesh is moving. The artificial compressibility formulation is utilized with a dual time stepping approach for accurate time integration. The gradient smoothing operation is utilized based on carefully designed node/mid-point associated gradient smoothing domains for the 1st-/2nd-order spatial approximations of the field variables at the nodes. To ensure the spatial stability, the 2nd-order Roe flux differencing splitting unwinding scheme is adopted to deal with the convective flux. Convergence, accuracy and robustness of the proposed method, i.e. GSM/ALE, are examined through a series of benchmark tests. Numerical results show that the proposed method can preserve the 2nd-order spatial/temporal accuracies, and produce reliable results even on extremely distorted mesh. Good agreement of calculated results with the reference ones in several examples indicates the robustness of the proposed method for solving fluid–rigid body interaction problems.