Fast, Conservative Schemes for the Full Potential Equation Applied to Transonic Flows

Holst, Terry L.; Ballhaus, W. F.

doi:10.2514/3.61088

Cited by 78 publications

(24 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since this work, many calculations using AF iteration schemes have been obtained including a number of other efforts from Ames: Goorjian [18], and Steger and Caradonna [19] for time-accurate full potential applications; Ballhaus et al [20] for steady two-dimensional TSD computations; Holst and Ballhaus [14], and Holst [15] for steady two-dimensional full potential computations; and Holst and Thomas [21] for three-dimensional full potential computations.…”

Section: Steady Full Potential Equation Methodsmentioning

confidence: 98%

“…One such approach, which uses an upwind evaluation of the density to stabilize supersonic regions of flow, is the artificial density scheme. One variation of this scheme, developed by Holst and Ballhaus [14] and Holst [15,16], is given by (for the two two-dimensional full potential equation in transformed coordinates)…”

Section: Steady Full Potential Equation Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Transonic flow potential method development at Ames research center

Holst

2009

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

Section: Steady Full Potential Equation Methodsmentioning

confidence: 98%

Section: Steady Full Potential Equation Methodsmentioning

confidence: 99%

Transonic flow potential method development at Ames research center

Holst

2009

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

“…have been in use for some time, e.g., [6], [14], [17]. We now compare the x differencing in the algorithms of [6], [14], [17], with that of (4.4). Using E.O., we have (if 8X$ > 0 for all relevant points) Density Biasing.…”

Section: Nowmentioning

confidence: 99%

“…In this section we shall give examples of schemes of the type (3.6), where the function h is an E flux. We shall compare these flux biasing algorithms, with the density biasing methods of [6], [14], and [17].…”

mentioning

confidence: 99%

Entropy condition satisfying approximations for the full potential equation of transonic flow

Osher

Hafez²,

Whitlow

1985

Math. Comp.

View full text Add to dashboard Cite

Abstract. We shall present a new class of conservative difference approximations for the steady full potential equation. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. We prove rigorously that these new schemes satisfy a new discrete "entropy inequality", which rules out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in our analysis is the construction of an "entropy inequality" for the full potential equation itself. We conclude by presenting results of some numerical experiments using our new schemes.I. Introduction. The full potential equation is a common model for describing supersonic and subsonic flow close to the speed of sound. The flow is assumed to be that of a perfect gas, and the assumptions of irrotationality and constant entropy are made. The resulting equation is a single nonlinear partial differential equation of second order, which changes type from hyperbolic to elliptic, as the flow goes from supersonic to subsonic. Flows with a supersonic component generally have solutions with shocks, so the conservation form of the equation is important.This formulation, (FP), is one of three conservative formulations used for inviscid transonic flows. The other two are transonic small-disturbance equation, (TSD), and Euler equation, (EU), which is the exact inviscid formulation. The FP formulation is the most efficient of the three in terms of accuracy-to-cost ratio for a wide range of inviscid transonic flow applications for real geometries. TSD is valid for thin wings at free stream Mach numbers near unity, and EU, while the least restrictive, involves the most complicated system of equations.During the last few years, many numerical calculations using FP have been presented, e.g., [19], [14], [17], and [6]. The object of our present investigation is twofold. First, we wish to put the theory of nonlinear difference approximations to FP on a sound theoretical basis, via an "entropy condition", as described below. Second, we introduce a new class of entropy condition satisfying approximations, which are, in general, no more complicated to program than the usual density

show abstract

“…This paved the way for numerical solution of the full potential equations applicable to inviscid compressible flows with weak shock waves. Jameson (1973) performed an early calculation of a three-dimensional transonic flow over a yawed wing, and Holst and Ballhaus (1979) developed a numerical scheme for the full potential equation in conservation-law form.…”

Section: Algorithms and Meshingmentioning

confidence: 99%