An AUSM-based third-order compact scheme for solving Euler equations - Mohamad, Mahmod Abd Hakim; Basri, ShahNor; Abd. Rahim, Irfan; Mohamad, Musli (Federation of Engineering Institutions of Islamic Countries, 2006)
In this paper, a third-order compact upwind scheme is given for calculating flows containing discontinuities. The scheme utilizes the AUSM flux splitting method and a third-order compact upwind space discretization relation for calculating third-order numerical flux function. TVD shock capturing properties of the scheme are achieved through a minmod flux limiter. A multistage TVD Runge-Kutta method is employed for the time integration. Computations are performed for two typical one-dimensional problems containing shocks, namely, the steady flow in a divergent nozzle and the unsteady shock tube problem. First-order and third-order numerical results are presented in comparison with the exact solutions. Computed results with KFVS method are also presented.