SummaryIn the present study, the preconditioned incompressible Navier-Stokes equations with the artificial compressibility method formulated in the generalized curvilinear coordinates are numerically solved by using a high-order compact finite-difference scheme for accurately and efficiently computing the incompressible flows in a wide range of Reynolds numbers. A fourth-order compact finite-difference scheme is utilized to accurately discretize the spatial derivative terms of the governing equations, and the time integration is carried out based on the dual time-stepping method. The capability of the proposed solution methodology for the computations of the steady and unsteady incompressible viscous flows from very low to high Reynolds numbers is investigated through the simulation of different 2-dimensional benchmark problems, and the results obtained are compared with the existing analytical, numerical, and experimental data. A sensitivity analysis is also performed to evaluate the effects of the size of the computational domain and other numerical parameters on the accuracy and performance of the solution algorithm. The present solution procedure is also extended to 3 dimensions and applied for computing the incompressible flow over a sphere. Indications are that the application of the preconditioning in the solution algorithm together with the high-order discretization method in the generalized curvilinear coordinates provides an accurate and robust solution method for simulating the incompressible flows over practical geometries in a wide range of Reynolds numbers including the creeping flows.
| INTRODUCTIONThe development and application of an accurate and robust numerical solution procedure constructed based on a unified formulation to be capable of predicting the flowfield in a wide range of flow conditions are of prime interest because there will be no need to apply different formulations for different flow conditions that cause the complexity in the use of a complicated flow solver. Many physical problems involve the incompressible fluid flows, and therefore, the development of an accurate and robust solution algorithm constructed based on a unified formulation is applicable for computing the flowfield in a wide range of flow conditions from very low to high Reynolds numbers.
The characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary conditions. Two benchmark test cases are computed to investigate the accuracy and performance of the characteristic boundary conditions implemented compared to the simplified boundary conditions. The sensitivity of the solution obtained by applying the characteristic boundary conditions to the different numerical parameters is also studied. Indications are that the characteristic boundary conditions applied improve the accuracy and the convergence rate of the solution compared to the simplified boundary conditions.
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