High resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations

Hartwich, Peter; Hsu, C.-H.

doi:10.2514/6.1987-547

Cited by 13 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…delta wing, low Reynolds number, vortex flows Aerodynamics of slender delta wing with large swept angle, which is widely adopted in modern fighter aircrafts and missiles, has been investigated experimentally and numerically over decades. Nowadays, the flow characteristics of slender delta wing are well understood [1][2][3] , and the typical flow structures are as follows: The local separation from the leading edge generates a pair of counter-rotating primary vortices on the leeward surface of the wing, the leading-edge vortices spiral around the vortex axis and move downstream, the separated flow attaches on the leeward surface and induces secondary separation due to the vortex/wall interaction.The recent development of unmanned air vehicle (UAV) and micro air vehicle (MAV) has stimulated the investigation on low and moderate swept delta wings [4][5][6][7] . Generally speaking, the flow structures over these nonslender delta wings share some similarity with large swept wing, such as the leading-edge vortices and the separation-reattachment flow.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulations of leading-edge vortex core axial velocity for flow over delta wings

Chen

Wang

2009

Sci. China Ser. E-Technol. Sci.

View full text Add to dashboard Cite

Numerical simulations have been performed to investigate the characteristics of leading-edge vortex core axial velocity over two delta wings with leading edge swept angles Λ = 50°and 76°, respectively. It is obtained that Reynolds number has the most important effect on the axial velocity of the primary leading-edge vortex core. At Reynolds numbers larger than 10 5 , the jet-like flow of the vortex core is the most common type for both the large and the moderate swept delta wings. While if Reynolds number decreases to 10 3 -10 4 , the core axial velocity distributions for these two delta wings present the wake-like profile for all angles of attack considered in the present investigation. delta wing, low Reynolds number, vortex flows Aerodynamics of slender delta wing with large swept angle, which is widely adopted in modern fighter aircrafts and missiles, has been investigated experimentally and numerically over decades. Nowadays, the flow characteristics of slender delta wing are well understood [1][2][3] , and the typical flow structures are as follows: The local separation from the leading edge generates a pair of counter-rotating primary vortices on the leeward surface of the wing, the leading-edge vortices spiral around the vortex axis and move downstream, the separated flow attaches on the leeward surface and induces secondary separation due to the vortex/wall interaction.The recent development of unmanned air vehicle (UAV) and micro air vehicle (MAV) has stimulated the investigation on low and moderate swept delta wings [4][5][6][7] . Generally speaking, the flow structures over these nonslender delta wings share some similarity with large swept wing, such as the leading-edge vortices and the separation-reattachment flow. However, there exist some distinct differences, i.e., both experimental and numerical investigations have shown that the vortex structures over nonslender delta wings are formed much closer to the surface of the wing, and in some circumstance another pair of concentrated vortices might appear outside of the primary leading edge vortex, forming the so called dual vortex structures [4][5][6][7][8] . It is often assumed that the flow over slender delta wing has weak Reynolds number dependency. However, the flow structures and aerodynamic characteristics over low swept wing are sensitive to Reynolds number. The maximum of axial velocity at the vortex core over a slender wing could be several times larger than freestream velocity [3,9] , and the jet-like axial velocity profiles were observed upstream of the vortex breakdown position [3] . Ol and Gharib [10] conducted Particle Image Velocimetry (PIV) measurements for a 50° swept delta wing in water tunnel, and the wake-like axial velocity profiles were observed at low Reynolds number. However, the numerical simulation of flow over low swept delta wing conducted by Gordnier and Visbal [8] indicated the existence of both jet-like and wake-like velocity profiles.Although the previous studies have involved the vortical structures over low swept win...

show abstract

mentioning

confidence: 99%

mentioning

confidence: 99%

Numerical simulations of leading-edge vortex core axial velocity for flow over delta wings

Chen

Wang

2009

Sci. China Ser. E-Technol. Sci.

View full text Add to dashboard Cite

show abstract

“…The present point and line relaxation schemes are similar to those used by Rogers et al [10,19] but with slight modifications to the point relaxation scheme in the formation of the left-hand-side matrices and in the sweeping strategy. The author also tried the LU-SGS scheme [18,38] and the approximation factorization-planar symmetric Gauss-Seidel scheme [13] and found that the overall computing time was greater than that of the diagonalized ADI scheme; thus these implicit schemes were excluded in this work. The discretization for the convective terms used is an upwind differencing scheme based on Roe's approximate Riemann solver [39] with Van Leer's MUSCL formulation [40], which was applied to the ACM and recommended for its computational efficiency and accuracy in [11,31].…”

Section: Introductionmentioning

confidence: 99%

“…The upwind differencing schemes that have been used include the flux-differencing splitting [9,10], MUSCL [11,12], TVD [13,14], and WENO [15] schemes; the solution techniques that have been implemented cover the BeamWarming scheme [16,17], the approximation factorization-planar symmetric Gauss-Seidel scheme [13], lower-upper symmetric Gauss-Seidel (LU-SGS) scheme [15,18], line and point relaxation schemes [10,19], the explicit multistage Runge-Kutta method [20], and so on. The application is also extended to unsteady flow computations [9,10,20] by using a dual-time-stepping procedure that subiterates at each physical time step and drives the divergence of the velocity toward zero.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

2002

Journal of Computational Physics

View full text Add to dashboard Cite

To develop a robust and efficient computational flow simulation tool for incompressible flow applications, a number of different implicit multigrid schemes for solving the three-dimensional incompressible Navier-Stokes equations are compared in the current study. These schemes consist of a common full approximation storage (FAS) multigrid algorithm implemented in conjunction with three different implicit schemes, which include a modified point Gauss relaxation, a standard Gauss-Seidel line relaxation, and the Beam-Warming alternating direction implicit (ADI) scheme. The flow solver used in the study is based on artificial compressibility and uses a third-order upwind difference for the convective terms and a second-order central difference for the viscous terms. The efficiency of each implicit multigrid scheme is assessed in terms of the computing time required for two laminar flow problems: the entry flow through a 90• bent square duct, and the steady-state and unsteady flows past a prolate spheroid at incidence with an axis ratio of 4 : 1. It is found that implementation of Neumann boundary conditions on the coarse grid in terms of the flow variable correction rather than the flow variable itself is essential for obtaining good convergence in the collocated finite difference discretization. The results of steady-state flow computations show that all the implicit multigrid schemes yield more than 50% computational time savings over their single grid counterparts, and the point or line relaxation multigrid scheme outperforms the ADI multigrid scheme by at least a factor of 2. However, in unsteady flow computations, the computational time saving of the multigrid scheme is less than that in steady-state cases. The current study concludes that the FAS multigrid algorithm implemented with the modified point Gauss relaxation scheme is preferable for simulating both steady-state and time-dependent incompressible flows. c 2002 Elsevier Science (USA)

show abstract

“…Recently, this method is improved by introducing the efficient numerical techniques such as the linearization of Steger and Kutler (1977), diagonalization of Chang et al (1988), etc. and also extended to the orthogonal and generalized curvilinear coordinate system reported by Hartwich and Hsu (1988) and Dick (1989). The other widely used method for solving unsteady incompressible Navier-Stokes equations is the well known MAC (Marker and Cell) method developed by Harlow and Welch (1965) The basic equations are the unsteady NavierStokes equations for three-dimensional incompressible rotational flow which in term of relative velocity with respect to the rotational reference frame can be written as follows:…”

Section: Introductionmentioning

confidence: 99%

Three‐Dimensional Thermo Fluid Analysis of Large Scale Electric Motor

Biswas

Ishizuka

Iwasaki

1999

International Journal of Rotating Machinery

View full text Add to dashboard Cite

In the present work, the flow and temperature fields in large scale rotating electric motor are studied by solving the Navier-Stokes equations along with the temperature equation on the basis of finite difference method. All the equations are written in terms of relative velocity with respect to the rotating frame of reference. Generalized coordinate system is used so that sufficient grid resolution could be achieved in the body surface boundary layer region. Differential terms with respect to time are approximated by forward differences, diffusion terms are approximated by the implicit Euler form, convection terms in the Navier-Stokes equations are approximated by the third order upwind difference scheme. The results of calculation led to a good understanding of the flow behavior, namely, the rotating cavity flow in between the supporting bar of the motor, the flow stagnation and region of temperature rise due to flow stagnation, etc. Also the measured average temperature of the motor coil wall is predicted quite satisfactorily.

show abstract

High resolution upwind schemes for the three-dimensional incompressible Navier-Stokes equations

Cited by 13 publications

References 12 publications

Numerical simulations of leading-edge vortex core axial velocity for flow over delta wings

Numerical simulations of leading-edge vortex core axial velocity for flow over delta wings

Comparison of Implicit Multigrid Schemes for Three-Dimensional Incompressible Flows

Three‐Dimensional Thermo Fluid Analysis of Large Scale Electric Motor

Contact Info

Product

Resources

About