Unsteady Euler solutions for arbitrarily moving bodies and boundaries

A methodology for the computation of unsteady Euler flows in configuration s with moving boundaries is presented. The procedure is composed of a moving and adaptive grid management algorithm and a LagrangianEulerian flow solver. The domain discretization is handled via unstructured triangular grids. The flow scheme uses a generalized version of Roe's approximate Riemann solver, which takes into account the mesh movement while satisfying in an intrinsic way the geometric conservation laws. Grid-flow coupling is obtained through error estimation. The methodology is applied to various flow problems showing moving shock waves and moving geometries. MONG the many obstacles on the path toward the development of more advanced computational fluid dynamics (CFD) tools, the coupling between the discretization grid and the flow solver occupies an important place. Several layers have been added to the use of adaptive grids in terms of different adaptation strategies such as grid relocation, grid enrichment, and coarsening on structured and/or unstructured grids.1-5 In the case of steady flowfields, these methods have been very successful. For unsteady flow problems, such as compressible flows with moving boundaries and/or moving discontinuities, it is thought that the use of such methods is inevitable. In fact, when rapid changes in the solution occur or when the computational domain itself evolves in time, it is almost impossible to design a unique and adequate grid for the whole computation process, and modifications in the grid connectivity become essential. This also necessitates the implementation of a numerical scheme that correctly handles grid movement. Along these lines, the approach presented by Ref. 4, based on a global remeshing strategy and a finite element flow solver, has shown great potential. In this work, a separate development is described. The focus is on a dynamic grid adaptation procedure that uses triangles as the basic discretization elements. The method, dedicated to the Euler system of equations, couples a finite volume flow solver with a local remeshing approach. The remeshing amalgamates several algorithms basically dedicated to grid motion, grid adaptation, grid quality control, and grid size control. These ingredients constitute fundamental elements for the simulation of flows in complex domains with substantial deformations of the boundaries and with large ratios between the areas of the largest and smallest triangles appearing in the discretization. The computational domain is defined by a set of curves whose kinematic hierarchy determines the grid pattern. The grid evolution is established on the basis of sequential operators related to the velocity of the moving curves and to nodal