A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

“…The intermediate stages (29) and (30) consist of two implicit steps and can be simplified by eliminating q (k) between (29) and (30) [10], and obtain a nonlinear elliptic equation for ρ (k) :…”

“…The WCNS's are first proposed by Deng and Zhang [21] based on the cell-centered compact scheme of Lele [28] and are developed in [22,23,24,29]. The expression of the classical cell-centered compact scheme is that a linear combination of the unknown approximations of the first derivative of a function at the grid points in a stencil is equal to another linear combination of the function itself at the grid points in the same stencil.…”

“…Roe's flux difference splitting method, van Leer's flux vector splitting and Liou's advection upstream splitting method, and flux derivatives can be computed by different explicit or implicit compact finite difference methods [23,29]. In this work, in view of the good performance of the IMEX time discretization method and the WC-NS's, we design a high order IMEX WCNS for the all-Mach isentropic Euler system based on the acoustic/advection splitting strategy [10].…”

High order semi-implicit weighted compact nonlinear scheme for the all-Mach isentropic Euler system

“…Recently a class of weighted compact nonlinear schemes (WCNS's) as high order accurate shock-capturing schemes have been widely adopted to investigate compressible flows with shock waves and discontinuities [19,20,21,22,23,24,25]. The WCNS's first proposed by Deng and Zhang [19] and developed in [20,21,22,26] integrate WENO interpolation into the cell-centered compact schemes. They are variants of the WENO schemes and have the good performance in terms of accuracy, robustness and efficiency for compressible flows.…”

Effect of Nonuniform Grids on High-Order Finite Difference Method

“…Recently, Rizzetta et al [5] carried out a high-order compact scheme with compact filter, which has been demonstrated to produce accurate and stable results in large eddy simulations. A family of hybrid dissipative compact schemes is proposed by Deng et al [9] and suitable for simulations in aeroacoustics. To make compact schemes possess the shock-capturing capabilities, many efforts have been devoted [10][11][12], which were well summarized by Shen and Zha [13].…”