A high efficient implicit discontinuous Galerkin method

In the introduction of the full paper, we point that, in our opinion, Cuckborn and Shu's Runge-Kutta discontinuous Galerkin method is good in calculation precision, but its slow convergence puts severe limits on its application to engineering problems. Therefore, we propose our efficient implicit scheme for accelerating convergence. In the iterative process, some important amendments are in application, which improve the efficiency significantly. At the same time, LU-SGS method is used to solve the large sparse linear system. By this means, subsonic and transonic flow over the airfoil is computed. It is found that this implicit scheme keeps unconditional stable for the subsonic and transonic flow. These results show preliminarily that, compared with the explicit scheme, our novel solver delivers a convergence rate that is approximately one order higher and much of the CPU time is saved.