Second-order time-accurate and geometrically conservative implicit schemesfor flow computations on unstructured dynamic meshes

We consider the solution of two- and three-dimensional flow problems with m oving boundaries using the Arbitrary Lagrangian Eulerian formulation or dyn amic meshes. We focus on the case where spatial discretization is performed by unstructured finite volumes and/or finite elements. We formulate the co nsequence of the Geometric Conservation Law on the second-order implicit te mporal discretization of the semi-discrete equations governing such problem s, and use it as a guideline to construct a new family of second-order time -accurate and geometrically conservative implicit numerical schemes for Row computations on moving grids. We apply these new algorithms to the solutio n of three-dimensional flow problems with moving and deforming boundaries, demonstrate their superior accuracy and computational efficiency, and highl ight their impact on the simulation of fluid/structure interaction problems . (C) 1999 Elsevier Science S.A. All rights reserved.