A Maximum-principle Preserving Nonlinear QUICK Scheme

In this paper,a maximum-principle preserving nonlinear quick scheme is proposed to approximate convective term of the conservation law.The nonlinear weight in the maximum-principle preserving nonlinear quick scheme is constructed in order to effectively capture smooth regions and discontinuities.The present numerical scheme use the firstorder upwind scheme near discontinuities and the QUICK scheme in smooth regions.The third-order Runge-Kutta method discretizes time for achieving the third-order accuracy.Numerical results demonstrate the present scheme can achieve the optimal order accuracy at extremal points of smooth regions of the solution and effectively avoid spurious near discontinuities.Then the error analysis and stability analysis of QUICK scheme show that error of this scheme is relatively small and the scheme is conditionally stable.