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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 structure of vortical flows. The accuracy and performance of the proposed solution procedure by applying the fourth-order compact finite-difference scheme are also examined by comparison with the solution obtained by the second-order central finite-difference scheme. Low-pass high-order filters are also applied to the fourth-order compact finite-difference scheme to investigate the performance of the vorticity confinement with the filtering scheme. The advection of a 2D isentropic vortex and a shock–vortex interaction problem are two test cases simulated for the assessment of the present solution methodology. The study shows that the high-order compact finite-difference schemes in conjunction with the vorticity confinement method can reasonably preserve the structure of vortical flows in coarse uniform Cartesian and curvilinear grids. Indications are that the present solution methodology is accurate and effective for solving compressible flow problems with vortical structures when coarse grids are used. [ABSTRACT FROM AUTHOR]