Instability of numerical solutions of the steady, supersonic blunt-body problem.

AIAA Journal ◽  
1967 ◽  
Vol 5 (5) ◽  
pp. 1035-1037 ◽  
Author(s):  
CZESLAW P. KENTZER
Keyword(s):  
Body Problem ◽  
Blunt Body ◽  
Numerical Solutions

Numerical analysis of the viscous, hypersonic, MHD blunt-body problem.

AIAA Journal ◽  
1973 ◽  
Vol 11 (3) ◽  
pp. 383-384 ◽  
Author(s):  
CHONG-YUL YOO ◽  
ROBERT W. PORTER
Keyword(s):  
Numerical Analysis ◽  
Body Problem ◽  
Blunt Body

Spectral methods for the Euler equations - The blunt body problem revisited

AIAA Journal ◽  
1991 ◽  
Vol 29 (9) ◽  
pp. 1458-1462 ◽  
Author(s):  
David A. Kopriva ◽  
Thomas A. Zang ◽  
M. Yousuff Hussaini
Keyword(s):  
Euler Equations ◽  
Spectral Methods ◽  
Body Problem ◽  
Blunt Body

A comparison of solutions to a blunt body problem.

AIAA Journal ◽  
1966 ◽  
Vol 4 (8) ◽  
pp. 1425-1426 ◽  
Author(s):  
JAMES C. PERRY ◽  
LIONEL PASIUK
Keyword(s):  
Body Problem ◽  
Blunt Body

A conformal mapping approach to the blunt body problem.

AIAA Journal ◽  
1967 ◽  
Vol 5 (11) ◽  
pp. 2047-2048 ◽  
Author(s):  
HENRY S. SANEMATSU ◽  
ROBERT L. CHAPKIS
Keyword(s):  
Conformal Mapping ◽  
Body Problem ◽  
Blunt Body ◽  
Mapping Approach

scholarly journals The use of Kepler solver in numerical integrations of quasi-Keplerian orbits

2020 ◽  
Vol 496 (3) ◽  
pp. 2946-2961
Author(s):  
Chen Deng ◽  
Xin Wu ◽  
Enwei Liang
Keyword(s):  
Body Problem ◽  
Numerical Solutions ◽  
Phase Error ◽  
Integral Invariant ◽  
True Anomaly ◽  
Integration Time ◽  
Angular Momentum Vector ◽  
Orbital Elements ◽  
Eccentric Anomaly ◽  
Two Body Problem

ABSTRACT A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the eccentric anomaly relies on the true anomaly that is associated with a unit radial vector calculated by an integrator. This scheme rigorously conserves all integrals and orbital elements except the mean longitude. However, the Kepler energy, angular momentum vector, and Laplace–Runge–Lenz vector for perturbed Kepler problems are slowly varying quantities. However, their integral invariant relations give the quantities high-precision values that directly govern five slowly varying orbital elements. These elements combined with the eccentric anomaly determine the desired numerical solutions. The newly proposed method can considerably reduce various errors for a post-Newtonian two-body problem compared with an uncorrected integrator, making it suitable for a dissipative two-body problem. Spurious secular changes of some elements or quasi-integrals in the outer Solar system may be caused by short integration times of the fourth-order Runge–Kutta algorithm. However, they can be eliminated in a long integration time of 108 yr by the proposed method, similar to Wisdom–Holman second-order symplectic integrator. The proposed method has an advantage over the symplectic algorithm in the accuracy but gives a larger slope to the phase error growth.

Boundary layer over spinning blunt body of revolution at incidence including Magnus forces

1978 ◽  
Vol 363 (1714) ◽  
pp. 357-380 ◽  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Blunt Body ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Meridional Flow ◽  
Meridional Plane ◽  
Magnus Force ◽  
Displacement Thickness

An incompressible laminar flow over a spinning blunt-body at incidence is investigated. The approach follows strictly the three-dimensional boundary layer theory, and the lack of initial profiles is readily resolved. The rule of the dependence zone is satisfied with the Krause scheme, and complete numerical solutions are obtained for an ellipsoid of revolution at 6° incidence and two spin rates. Spinning causes asymmetry which, in turn, introduces the Magnus force. The asymmetry is most pronounced in crossflow, but is also noticeable in the skin friction and displacement thickness of the meridional flow. A variety of crossflow profiles are determined as are the streamline patterns in the cross- and meridional-plane which are especially useful in visualizing the flow structure. Detailed distribution of skin friction, displacement thickness, and centrifugal pressure are presented. A negative crossflow displacement thickness is found to be physically meaningful. The Magnus forces due to the crossflow skin friction and the centrifugal pressure are determined; these two forces partly compensate for each other. At lower spin rate, the frictional force is larger, resulting in a positive Magnus force. At high spin rate, the opposite is obtained. At high incidence (30°) the present boundary layer calculations could be carried out in the longitudinal direction, only up to the beginning of an open separation.

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