Second-order, far-field computational boundary conditions for inviscid duct flow problems

Verhoff, A.; Stookesberry, D.

doi:10.2514/3.11060

Cited by 14 publications

(2 citation statements)

References 7 publications

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“…The asymptotic form of Eqs. (1) in the far field becomes Using the definition (3) and the algebraic total temperature relation (2). the far field Mach number M, can be expressed as The exact solution, however, can be obtained if necessary by asymptotic iterative corntion, since R, and Rz are small and well-behaved in the region exterior to the boundary.…”

Section: Analytic Formulationmentioning

confidence: 99%

First-order far field computational boundary conditions for O-grid topologies

Verhoff¹

1995

33rd Aerospace Sciences Meeting and Exhibit

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First-order far field computational boundary conditions for inviscid external flow problems have been developed for 0-grid topologies. These boundary conditions are derived from analytic solutions of an asymptotic form of the steady state Euler equations and have improved accuracy compared to commonly-used characteristic boundary conditions. The Euler equations are asymptotically linearized about a constant pressure, rectilinear flow condition which truly represents conditions at infmity. Previous work had developed fit-order boundary conditions for C-grid topologies by assuming small perturbations in both pressure and flow direction at and beyond the computational boundary, by decoupling the inflow and outflow analyses, and by linearizing the thermodynamic relations. The present work lifts these restrictions, although higher-order compressibility effects are neglected. Because the Euler equations are used to develop the boundary conditions, the flow crossing the boundary can be rotational. The boundary conditions can be used with any numerical Euler solution method and allow computational boundaries to be located very close to the nonlinear region of interest. This leads to a significant reduction in the number of grid points required for numerical solution. Numerical results are presented which show that the boundary conditions and far field analytic solutions provide a smooth mansition across a computational boundary to the m e far field conditions at infinity. They also demonstrate the synergism that can be realized from coupling analytic and computational methods.

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Section: Analytic Formulationmentioning

confidence: 99%

First-order far field computational boundary conditions for O-grid topologies

Verhoff¹

1995

33rd Aerospace Sciences Meeting and Exhibit

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“…The solution converges after about 5500 iterations with a CFL number of 0.50 (see Figure 14). The calculated Mach number and ow angle contours by the present code and that of Verho [12] are shown in Figures 15-18. Mach number distributions along the lower and upper walls are shown in Figure 19.…”

Section: Sinusoidal Bump (2d)mentioning

confidence: 99%

Characteristic Euler shock‐fitting formulation for multi‐dimensional flows

Başeşme¹,

Akmandor²,

Ucer³

2003

Numerical Methods in Fluids

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SUMMARYA three-dimensional explicit time marching algorithm has been developed for the numerical solution of inviscid internal ows. The formulation uses the natural streamline co-ordinate system. The unsteady Euler equations in non-conservative form are expressed in terms of the extended Riemann variables and the ow angles. Along the characteristic trajectories in the space-time domain, these equations reduce to a system of ordinary di erential equations. Boundary conditions are also implemented in characteristic form. Shock waves are calculated after performing a one-point shock correction that maintains conservation across the discontinuity.The algorithm has been applied to subsonic, transonic and supersonic test cases. Despite the wide range in the Mach number and the diversity of the tested ow geometries, close agreement have been obtained with available analytical and numerical results.

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Finite element schemes for non-linear problems in infinite domains

Givoli

Patlashenko

1998

Int. J. Numer. Meth. Engng.

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A class of non-linear elliptic problems in inÿnite domains is considered, with non-linearities extending to inÿnity. Examples include steady-state heat radiation from an inÿnite plate, and the de ection of an inÿnite membrane on a non-linear elastic foundation. Also, this class of problems may serve as a starting point for treating non-linear wave problems. The Dirichlet-to-Neumann (DtN) Finite Element Method, which was originally developed for linear problems in inÿnite domains, is extended here to solve these non-linear problems. Several DtN schemes are proposed, with a trade-o between accuracy and computational e ort. Numerical experiments which demonstrate the performance of these schemes are presented. ? 1998 John Wiley & Sons, Ltd.

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Second-order, far-field computational boundary conditions for inviscid duct flow problems

Cited by 14 publications

References 7 publications

First-order far field computational boundary conditions for O-grid topologies

First-order far field computational boundary conditions for O-grid topologies

Characteristic Euler shock‐fitting formulation for multi‐dimensional flows

Finite element schemes for non-linear problems in infinite domains

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