Multi-moment finite volume method for incompressible flows on unstructured moving grids and its application to fluid-rigid body interactions

Abstract

Multi-moment finite volume method for unsteady incompressible flows on unstructured moving grids is developed under the Arbitrary Lagrangian Eulerian (ALE) framework. Two moments, volume integrated average (VIA) and point values (PV), are treated as computational variables which allow to construct quadratic or higher-order polynomials within a compact stencil. The VIAs are computed by a finite volume method (FVM) that ensures the rigorous numerical conservativeness, while the PVs are defined at cell vertices and updated efficiently by a formulation based on the governing equations in a differential form. By employing PVs at cell vertices as additional variables updated at each time step, the present multi-moment finite volume method shows great advantage when applied to the ALE framework for interactions among multiple materials, where the solution points can always coincide with the interfaces between different materials. Thus, any extra numerical step to approximate the values onto the interfaces is not necessary. We have devised two coupling schemes, i.e. an explicit weak coupling scheme and a semi-implicit strong coupling scheme, to formulate the interactions between fluid and moving solid with a wide range of mass ratios. An accurate and robust fluid-solid interaction (FSI) solver has been built by integrating the above numerical components with a radial basis function (RBF) interpolation technique for mesh movement. We in this paper present various benchmark tests to extensively verify the proposed numerical solver, which demonstrate its appealing performance in solving a large class of FSI problems.