Development of targeted compact nonlinear scheme with increasingly high order of accuracy

In this paper we present general formulation of targeted compact nonlinear scheme (TCNS) with increasing order of accuracy. This new scheme introduces the incremental-size and ENO-like stencil selection of targeted essentially non-oscillatory (TENO) scheme to weighted compact nonlinear scheme (WCNS). Other aim of the paper is construction of new global smoothness indicators (GSI) for TCNS. We used various benchmark problems of scalar hyperbolic equations and system of Euler equations for investigation of performance of TCNS and new GSIs.