A priori subcell limiting based on compact nonuniform nonlinear weighted schemes of high-order CPR method for hyperbolic conservation laws

This paper develops a shock capturing approach for high-order correction procedure via reconstruction (CPR) method with Legendre-Gauss solution points. Shock regions are treated by novel compact nonuniform nonlinear weighted (CNNW) schemes, which have the same points as CPR method. CNNW schemes constructed discretizing flux derivatives based on Riemann fluxes at in one cell and using (NNW) interpolations to obtain left right values Then, priori subcell p-adaptive limiting of is proposed hyperbolic conservation laws. Firstly, troubled indicator used detect quantify smoothness. Secondly, according magnitude indicator, varying accuracy orders chosen adaptively cells. The spectral property discrete laws mathematically analyzed. Various numerical experiments show that has superiority satisfying good balance between resolution robustness.