A fully implicit method for steady and unsteady viscous flow simulations

In this paper a time-accurate, fully implicit method has been applied to solve a variety of steady and unsteady viscous flow problems. It uses a finite volume cell-centred formulation on structured grids and employs central space discretization with artificial dissipation for the residual computation. In order to obtain a second-order time-accurate implicit scheme, a Newton-like subiteration is performed in the original LU-SGS method to converge the calculations at each physical time step by means of a dual-time approach proposed by Jameson. The numerical experiments show that the present method is very efficient, reliable, and robust for steady and unsteady viscous flow simulations, especially for some low speed flow problems.