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The main goal of this study is to assess the application of high-order compact finite-difference schemes for the solution of the Euler equations in conjunction with the compressible vorticity confinement method on both uniform Cartesian and curvilinear grids. Here, the spatial discretization of the governing equations is performed by the fourth-order compact finite-difference scheme and the temporal term is discretized by the fourth-order Runge-Kutta method. To stabilize the numerical solution, appropriate dissipation terms are applied and a detail assessment is performed to study the effects of the values of confinement and dissipation coefficients on the solution to reasonably preserve the... 

This paper uses a fourth-order compact finite-difference scheme for solving steady incompressible flows. The high-order compact method applied is an alternating direction implicit operator scheme, which has been used by Ekaterinaris for computing two-dimensional compressible flows. Herein, this numerical scheme is efficiently implemented to solve the incompressible Navier-Stokes equations in the primitive variables formulation using the artificial compressibility method. For space discretizing the convective fluxes, fourth-order centered spatial accuracy of the implicit operators is efficiently obtained by performing compact space differentiation in which the method uses block-tridiagonal...