A local domain-free discretization method to simulate three-dimensional compressible inviscid flows
In this paper, the domain-free discretization method (DFD) is extended to simulate the three-dimensional compressible inviscid flows governed by Euler equations. The discretization strategy of DFD is that the discrete form of governing equations at an interior point may involve some points outside the solution domain. The functional values at the exterior-dependent points are updated at each time step by extrapolation along the wall normal direction in conjunction with the wall boundary conditions and the simplified momentum equation in the vicinity of the wall. Spatial discretization is achieved with the help of the finite element Galerkin approximation. The concept of 'osculating plane' is adopted, with which the local DFD can be easily implemented for the three-dimensional case. Geometry-adaptive tetrahedral mesh is employed for three-dimensional calculations. Finally, we validate the DFD method for three-dimensional compressible inviscid flow simulations by computing transonic flows over the ONERA M6 wing. Comparison with the reference experimental data and numerical results on boundary-conforming grid was displayed and the results show that the present DFD results compare very well with the reference data. Copyright (c) 2009 John Wiley & Sons, Ltd.
domain-free discretization compressible inviscid flows boundary conditions non-boundary-conforming methods