• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.881-898
• /
• 2018

This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2008.05a
• /
• pp.1624-1629
• /
• 2008

The governing equations in generalized curvilinear coordinates for a 3D pulsatile flow are the Incompressible Navier-Stokes (INS) equations with the artificial dissipative terms and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. This method adopts a dual or pseudo time-stepping Artificial Compressibility (AC) method integrated in pseudo-time. The computational technique implements the implicit approximate factorization method of the Beam and Warming method (1978), which is the extension of the Alternate Direction Implicit (ADI) method. The algorithm yields practically identical velocity profiles and secondary flows that are in excellent overall agreement with an experimental measurement (Rindt & Steenhoven, 1991).

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
• /
• 1992.08a
• /
• pp.16-19
• /
• 1992

최근 컴퓨터의 발달과 함께 해안공학과 관련된 문제 해결에 있어서 처리속도에 관한 제약성은 점차 감소되고 있는 반면 정확도에 관한 관심이 높아지고 있는 추세이다. 현재까지 조석파 해석에서 가장 널리 쓰이고 있는 ADI(alternate direction implicit) 방법도 한 방향으로만 음해법적으로 차분하게 되므로 지형이 복잡한 곳에서는 소위 ADI효과라 불리는 바람직하지 않은 수치특성으로 인해 그 한계가 드러나고 있는 실정이다.(중략)

• International Journal of Aeronautical and Space Sciences
• /
• v.2 no.2
• /
• pp.28-38
• /
• 2001

A numerical method for the assessment and correction of tunnel wall interference effects on forced-oscillation testing is presented. The method is based on the wall pressure signature method using computed wall pressure distributions. The wall pressure field is computed using unsteady three-dimensional full Navier-Stokes solver for a 70-degree pitching delta wing in a wind tunnel. Approximately-factorized alternate direction implicit (AF-ADI) scheme is advanced in time by solving block tri-diagonal matrices. The algebraic Baldwin-Lomax turbulence, model is included to simulate the turbulent flow effect. Also, dual time sub-iteration with, local, time stepping is implemented to improve the convergence. The computed wall pressure field is then imposed as boundary conditions for Euler re-simulation to obtain the interference flow field. The static computation shows good agreement with experiments. The dynamic computation demonstrates reasonable physical phenomena with a good convergence history. The effects of the tunnel wall in upwash and blockage are analyzed using the computed interference flow field for several reduced frequencies and amplitudes. The corrected results by pressure signature method agree well with the results of free air conditions.

• International Journal of Aeronautical and Space Sciences
• /
• v.12 no.4
• /
• pp.318-330
• /
• 2011

This paper investigates the convergence characteristics of the modified artificial compressibility method proposed by Turkel. In particular, a focus is mode on the convergence characteristics due to variation of the preconditioning factor (${\alpha}_u$) and the artificial compressibility (${\beta}$) in conjunction with an upwind method. For the investigations, a code using the modified artificial compressibility is developed. The code solves the axisymmetric incompressible Reynolds averaged Navier-Stokes equations. The cell-centered finite volume method is used in conjunction with Roe's approximate Riemann solver for the inviscid flux, and the central difference discretization is used for the viscous flux. Time marching is accomplished by the approximated factorization-alternate direction implicit method. In addition, Menter's k-${\omega}$ shear stress transport turbulence model is adopted for analysis of turbulent flows. Inviscid, laminar, and turbulent flows are solved to investigate the accuracy of solutions and convergence behavior in the modified artificial compressibility method. The possible reason for loss of robustness of the modified artificial compressibility method with ${\alpha}_u$ >1.0 is given.