Solution of the multidimensional compressible Navier-Stokes equations by a generalized implicit method

Briley, W. R.; McDonald, H.

doi:10.1016/0021-9991(77)90029-8

Cited by 378 publications

(57 citation statements)

References 13 publications

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“…For example, to alleviate the difficulty of solving an unfactored implicit scheme, indirect methods have been devised by many researchers. The alternating direction implicit (ADI) scheme by Beam and Warming [37] or Briley and McDonald [38] approximates the implicit operator in the unfactored scheme by a product of three one-dimensional operators. This scheme is unconditionally stable in two dimensions.…”

Section: Numerical Schemesmentioning

confidence: 99%

Computational challenges of viscous incompressible flows

2005

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Over the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to the rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low-speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly erXcienf CFD took become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews some of the successes made possible by advances in computational technologies dunng the same period, ana discusses some of &e current challenges faced in computing incompressible flows.

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Section: Numerical Schemesmentioning

confidence: 99%

Computational challenges of viscous incompressible flows

2005

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“…McDonald [30], which leads to a block tridiagonal system. However , the present method needs iteration to obtain the solution at each time step .…”

Section: T(r T)mentioning

confidence: 99%

“…The Before obtaining more detailed and q u a n t i t a t i v e l y useful results , further refinement and optimization of the computer code is worth considering. For example , a non -iterative , fully-implicit scheme , as use by Briley and McDonald [30], as well as a v ari able gr id si ze may be worth …”

Section: It Is Also Worth Mention Ing That Figure If Exhibits An Oscimentioning

confidence: 99%

Ignition and Flame Propagation in Sprays.

Ashgrizzadeh¹,

Sirignano²,

Yao³

1984

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“…(7)) diameter of propeller total energy per unit volume vector of flux quantities in ~-direction vector of flux quantities inon-direction vector of flux quantities in ~-direction vector of source terms created by cylindrical generalized coordinate transformation rothalpy unit normal vector of cylindrical coordinate system Jacobian or advance ratio, (Uoo/nD) generalized matrices leading edge alignment rotational speed, revolutions per second static pressure dynamic pressure, O.5Poov; components of Q vector dependent variable of integration blade tip radius independent variables, cylindrical coordinates physical velocity in z-direction contravariant velocity defined in Eq. (2) physical velocity in or r-direction contravariant velocity defined in Eq. (2) velocity vector, ui z + vir + wi.…”

Section: Nomenclaturementioning

confidence: 99%