An assessment of numerical solutions of the compressible Navier-Stokes equations

Shang, J. S.

doi:10.2514/6.1984-1549

Cited by 7 publications

(3 citation statements)

References 107 publications

(5 reference statements)

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“…Equations (14)(15)(16) are solved simultaneously locally to generate 50(7,7): (17) Equation (17) is the boundary condition at the interface for both viscous and inviscid regions. Using this boundary, repeated SLOR sweeps are made in the inviscid region to allow for the elliptic effects to be determined in the solution domain.…”

Section: Viscid-inviscid Couplingmentioning

confidence: 99%

“…These methods range from using the panel method for incompressible flow to the finite-difference equations (FDE) for the transonic flows. Of course, the choice of the best method is a function of the Presented as Paper 85-1505 at the AIAA Seventh Computational Fluid Dynamics Conference, Cincinnati, OH, July 15-17, 1985; received Oct. 16,1985; revision received Jan. 16,1986. This paper is declared a work, of the U.S. Government and is not subject to copyright protection in the United States.…”

Section: Introductionmentioning

confidence: 99%

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Development of an iterative boundary-layer-type solver for axisymmetric separated flows

Halim

1986

AIAA Journal

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A boundary-layer-type solver is developed for the numerical solution of axisymmetric separated flows. A new, fully implicit coupling scheme for the viscous and inviscid regions is demonstrated. This fully implicit coupling technique is similar to the work of Carter and of Veldman and an extension of an earlier work of Halim and Hafez. A comparison is made for the convergence rate using this new, fully implicit coupling technique and the semi-implicit coupling of Halim and Hafez. Numerical results using the fully implicit coupling are obtained for laminar incompressible separated flows, including a boattail and a series of trough geometries. Also, the nearwake flow problem is considered using the present formulation. A clear conclusion of this investigation is that the present scheme, using the fully implicit coupling method, converges at a faster rate than the semi-implicit coupling and the partially parabolized Navier-Stokes procedures.

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Section: Viscid-inviscid Couplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of an iterative boundary-layer-type solver for axisymmetric separated flows

Halim

1986

AIAA Journal

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“…In numerical simulations, only different boundary conditions generate different physics from an identical governing equation system. 19 The fidelity to physics is also determined by the accuracy of initial and boundary values as well as the manner in which they are implemented. It may be obvious that developing a rigorous and systematic procedure for numerical boundary conditions across an interface of two media should be a pacing item in computational electromagnetics research.…”

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confidence: 99%

Scattered electromagnetic field of a re-entry vehicle

Shang

Gaitonde

1995

Journal of Spacecraft and Rockets

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Scattered electromagnetic fields around the X24C lifting body illuminated by both transverse electric and transverse magnetic incident plane waves are simulated. The refractive and diffractive phenomena are studied in the resonant and the optical regimes. The numerical solutions are generated by solving the three-dimensional Maxwell equations in the time domain using an upwind-biased finite-volume algorithm. The numerical results are third order accurate in space and second order accurate in time. The simulations are validated on simpler shapes, including a cylinder and a sphere, for which the solutions are well known. The scattered field is then described for the re-entry vehicle in the resonant and optical regimes. The numerical results demonstrate that accurate radar cross sections can be obtained by implementation of consistent boundary conditions developed for a perfectly conducting scatterer. Nomenclature B = magnetic flux density, Wb/m 2 D = electric displacement, C/m 2 E = electric field intensity, V/m 2 / = wave frequency, s" 1 H = magnetic flux intensity, A/m i, 7, k = index of discretized volume J = electric current density, A/m 2 n = outer normal of a surface R = numerical residual r, 0, $ = spherical coordinates t -time, s U = dependent variables V = elementary cell volume, m 3 € = electric permittivity, F/m X = wavelength, m 41 = magnetic permeability, H/m §» *?» £ = general curvilinear coordinates a) = angular frequency of wave, s" 1 Subscripts ch = characteristic time required for wave to traverse one body length = incident field property Superscripts +, -= flux vector associated with positive and negative eigenvalue

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Modelling of three-dimensional shock wave turbulent boundary layer interactions

Knight

Macroscopic Modelling of Turbulent Flows

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An assessment of numerical solutions of the compressible Navier-Stokes equations

Cited by 7 publications

References 107 publications

Development of an iterative boundary-layer-type solver for axisymmetric separated flows

Development of an iterative boundary-layer-type solver for axisymmetric separated flows

Scattered electromagnetic field of a re-entry vehicle

Modelling of three-dimensional shock wave turbulent boundary layer interactions

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