A new velocity reconstruction algorithm for multiphase flows with moving bodies

A new velocity reconstruction scheme is proposed to reconstruct the cell-centered velocity field with second-order accuracy through the given surface field of velocity vectors, and then incorporated into a high-fidelity numerical model to solve the incompressible Navier–Stokes equations in the arbitrary Lagrangian-Eulerian (ALE) formulation on unstructured grids. Different from the conventional model that reconstructs the centroidal velocity variation from the surface normal pressure gradients with the conventional balanced-force (CBF) algorithm in the entire domain, the present model employs two different schemes in the interface and non-interface regions. In the interface region, the cell-centered velocity variation is reconstructed with the surface normal pressure gradients calculated by the generic balanced-force (GBF) algorithm to suppress the non-physical flow generated by the imbalanced discretization between pressure gradient and external forces with CBF algorithm on non-orthogonal grids; In the non-interface region, the proposed second-order velocity reconstruction scheme for velocity variation is enabled by acquiring the surface field of pressure gradient vectors with adequate precision through the modification of pressure Poisson equation. The resulting model is able to effectively suppress the instability induced by the mesh deformation and the nonlinearity in fluid-structure interaction (FSI), and capture the flow structure with satisfactory energy conservation and higher accuracy. Various numerical examples have demonstrated that the present algorithm and computational framework offer a promising platform to provide more accurate and robust predictions of the flow field and the rigid body motion for multiphase FSI flows on unstructured grids.