A locally implicit second order accurate difference scheme for solving 2D time-dependent hyperbolic systems and Euler equations Original Research Article

The new difference method for solving 2D time-dependent hyperbolic systems and Euler equations is presented. This method is based on the unique difference scheme. The scheme is upwind quasi-monotone and provides second order accuracy both in space and time. The proposed scheme becomes implicit if and only if the corresponding Courant number is more than one. It should be pointed out that, as a rule, the scheme is implicit with respect with some variables and it is explicit with respect to others. The method is directed to solve problems that involve cells with a large aspect ratio. The efficiency of the scheme is demonstrated by numerical results.