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This paper uses a fourth-order compact implicit operator scheme for solving 2D/3D steady incompressible flows using the artificial compressibility method. To stabilize the numerical solution, numerical dissipation terms and/or filters are used. Results obtained for test cases are in good agreement with the available numerical and experimental results. A sensitivity study is also conducted to evaluate the effects of grid resolution and pseudocompressibility parameter on accuracy and convergence rate of the solution. The effects of filtering and numerical dissipation on the solution are also investigated  

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... 

In the present study, a truly incompressible smoothed particle hydrodynamics based on the artificial compressibility method for simulating steady and unsteady incompressible flows is proposed and assessed. The incompressible Navier–Stokes equations in the primitive variables formulation using the artificial compressibility method proposed by Chorin in the Eulerian reference frame are written in a Lagrangian reference frame to provide an appropriate incompressible SPH algorithm. The proposed SPH formulation implemented here is based on an implicit dual-time stepping scheme to be capable of time-accurate analysis of unsteady flows. The advantage of the Artificial Compressibility-based...