Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes Original Research Article

We consider the solution of two- and three-dimensional flow problems with moving boundaries using the Arbitrary Lagrangian Eulerian formulation or dynamic meshes. We focus on the case where spatial discretization is performed by unstructured finite volumes and/or finite elements. We formulate the consequence of the Geometric Conservation Law on the second-order implicit temporal discretization of the semi-discrete equations governing such problems, and use it as a guideline to construct a new family of second-order time-accurate and geometrically conservative implicit numerical schemes for flow computations on moving grids. We apply these new algorithms to the solution of three-dimensional flow problems with moving and deforming boundaries, demonstrate their superior accuracy and computational efficiency, and highlight their impact on the simulation of fluid/structure interaction problems.