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The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter... 

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... 

A high-order accurate implicit operator scheme is used to solve steady incompressible slip flow and heat transfer in 2D microchannels. The present methodology considers the solution of the Navier-Stokes equations using the artificial compressibility method with employing the Maxwell and Smoluchowski boundary conditions to model the slip flow and temperature jump on the walls in microchannels. Since the slip and temperature jump boundary conditions contain the derivatives of the velocity and temperature profiles, using the compact method the boundary conditions can be easily and accurately implemented. The computations are performed for a 2D microchannel and a 2D backward facing step in the... 

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  

The current study investigates the conjugate heat transfer characteristics for laminar flow in backward facing step channel. All of the channel walls are insulated except the lower thick wall under a constant temperature. The upper wall includes a insulated obstacle perpendicular to flow direction. The effect of obstacle height and location on the fluid flow and heat transfer are numerically explored for the Reynolds number in the range of 10 ≤ Re ≤ 300. Incompressible Navier-Stokes and thermal energy equations are solved simultaneously in fluid region by the upwind compact finite difference scheme based on flux-difference splitting in conjunction with artificial compressibility method. In... 

The current study investigates the conjugate heat transfer characteristics for laminar flow in backward facing step channel. All of the channel walls are insulated except the lower thick wall under a constant temperature. The upper wall includes a insulated obstacle perpendicular to flow direction. The effect of obstacle height and location on the fluid flow and heat transfer are numerically explored for the Reynolds number in the range of 10 ≤ Re ≤ 300. Incompressible Navier-Stokes and thermal energy equations are solved simultaneously in fluid region by the upwind compact finite difference scheme based on flux-difference splitting in conjunction with artificial compressibility method. In... 

In 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... 

The Eulerian methods are susceptible to generate the nonphysical spurious currents in the multiphase flow simulations near the interfaces. This paper presents a new Eulerian method to accurately simulate the velocity fields, especially near the multiphase flow interfaces and prevents the numerical results from generating the nonphysical currents. A Eulerian central difference finite-volume scheme equipped with the suitable numerical dissipation terms is used to simulate incompressible multiphase flows. The interface is captured by Flux Corrected Transport-Volume of Fluid method (FCT-VOF). Increasing the accuracy near the sharp gradients, such as interface, the conservative form of... 

In this work, a high-order nodal discontinuous Galerkin method (NDGM) is developed and assessed for the simulation of 2D incompressible flows on triangle elements. The governing equations are the 2D incompressible Navier–Stokes equations with the artificial compressibility method. The discretization of the spatial derivatives in the resulting system of equations is made by the NDGM and the time integration is performed by applying the implicit dual-time stepping method. Three numerical fluxes, namely, the local Lax–Friedrich, Roe and AUSM+-up are formulated and applied to assess and compare their accuracy and performance in the simulation of incompressible flows using the NDGM. Several... 

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...