Rayleigh's Problem at Low Mach Number According to the Kinetic Theory of Gases

Yang, H. T.

doi:10.1002/sapm1956351195

Cited by 31 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) ] which determines how to update the determinant of the covariance matrix when a measurement is incorporated. For the usual case of the measurement being of smaller dimension than the state, this result offers computational advantages because of the reduction of the order of the determinants to be evaluated.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, a "dummy" or "interference" probe having a diameter equal to 16% of the cone base diameter was brought into the recirculation region and was found to have very little effect on the measured pitot pressures. 1 Since the interference probe was much larger than any of the measurement probes, it was concluded that the measurement probes alone did not create significant disturbances in the base flow.…”

Section: Some Experiments In the Nearmentioning

confidence: 99%

“…1 The tube was faired smoothly into the nose of each cone, and served to carry gas that was ejected at various rates from the cone base. The dimensions of the models are shown in Fig.…”

Section: Some Experiments In the Nearmentioning

confidence: 99%

See 2 more Smart Citations

Rayleigh's problem at low Mach numbers based on kinetic theory.

Giddens

Huang

1967

AIAA Journal

View full text Add to dashboard Cite

we have detP J^ " detP' Rewriting Eq. (12), = I -KH T P'HKT =/•-/)" (32) (33) ;)Applying Eq. (27) and rearranging terms,From Eq. (12) detK(R (detK) 2 = (36) (37) Combining Eqs. (32, 35, and 37) gives the final result, Eq.CD. SummaryAn expression has been derived [Eq.(1) ] which determines how to update the determinant of the covariance matrix when a measurement is incorporated. For the usual case of the measurement being of smaller dimension than the state, this result offers computational advantages because of the reduction of the order of the determinants to be evaluated. Even greater computational savings are possible for stationary measurement statistics or for one-dimensional measurements. The results found by Cercignani et al. are exact analytical solutions, and the case considered by Chu is nonlinear. The purpose of this paper is twofold: first, to present a solution to the Rayleigh problem; and second, to demonstrate the accuracy and utility of the discrete ordinate method for linearized, time-dependent problems. Since many practical situations will not readily yield analytical solutions, the results presented in this study indicate that the method of discrete ordinates offers a promising tool for the numerical solution of transient problems. This method has been sue-

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Some Experiments In the Nearmentioning

confidence: 99%

See 1 more Smart Citation

Rayleigh's problem at low Mach numbers based on kinetic theory.

Giddens

Huang

1967

AIAA Journal

View full text Add to dashboard Cite

show abstract

“…The Rayleigh problem, as described by Yang and Lees [1956] and solved numerically by Bird [1976], was chosen as the problem of interest because of its simplicity and the published results with which to compare. Further, the scalar algorithm is given in Appendix G of [Bird 1976].…”

Section: Physical Applicationmentioning

confidence: 99%

Vectorized Monte Carlo molecular aerodynamics simulation of the Rayleigh problem

Pryor

Burns

1989

J Supercomput

View full text Add to dashboard Cite

A fully vectorized version of a Monte Carlo algorithm applied to molecular aerodynamics is presented. The algorithm is applied to the one-dimensional Rayleigh problem, an impulsively accelerated, heated flat plate, and is implemented on the CYBER 205. Issues relating to the details of vectorization, including the use of bit-type vectors, the maintaining of long vector lengths, and vector gather/scatter use, are discussed. Timings as functions of problem size are presented for various facets of the algorithm, and the problem of the "tail" due to stragglers is examined and quantified. Asymptotic speedup factors due to vectorization in the neighborhood of 7 to 8 are reported, depending upon problem parameters. The results indicate that, under certain circumstances, the problem performs well on vector architectures.

show abstract

“…In rarefied gas dynamics, the most classical problem of this type is the linearized Rayleigh problem (e.g. Yang & Lees 1956; Gross & Jackson 1958; Cercignani & Sernagiotto 1964; Sone 1964), which is described as follows. Suppose that a rarefied gas is initially at equilibrium with an infinite plane at rest which is maintained at a uniform and constant temperature.…”

Section: Introductionmentioning

confidence: 99%