Difference Schemes in an Arbitrary Curvilinear Coordinate System

1983 ◽  
pp. 118-125
Author(s):  
Yu. I. Shokin
Keyword(s):  
Coordinate System ◽  
Difference Schemes ◽  
Curvilinear Coordinate System ◽  
Curvilinear Coordinate

Flow Over a Cylinder at a Plane Boundary—A Model Based Upon (k–ε) Turbulence

1989 ◽  
Vol 111 (4) ◽  
pp. 414-419 ◽  
Author(s):  
T. Solberg ◽  
K. J. Eidsvik
Keyword(s):  
Pressure Gradient ◽  
Coordinate System ◽  
Adverse Pressure Gradient ◽  
Plane Boundary ◽  
Length Scale ◽  
Two Dimensional ◽  
Curvilinear Coordinate System ◽  
Recirculating Flow ◽  
Model Based ◽  
Curvilinear Coordinate

A model for two-dimensional flows over a cylinder at a plane boundary is developed. The model, based upon a (k-ε) turbulence closure, is formulated in a curvilinear coordinate system based upon frictionless flow. A length scale modification in areas of adverse pressure gradient and recirculating flow appears to be more realistic than the standard (k-ε) model. The main features of the predicted flow do not depend critically upon the details of the grid or model, which means that a well defined solution is obtained. The solution appears to be reasonable and validated to the extent that the data permits.

scholarly journals The partial banana mapping: a robust linear method for impact probability estimation

2019 ◽  
Vol 492 (3) ◽  
pp. 4546-4552
Author(s):  
Dmitrii E Vavilov
Keyword(s):  
Coordinate System ◽  
Confidence Region ◽  
Linear Method ◽  
Probability Estimation ◽  
Curvilinear Coordinate System ◽  
The Earth ◽  
Curvilinear Coordinate ◽  
Near Earth Asteroids ◽  
The Impact ◽  
Confidence Ellipsoid

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

Sign in / Sign up

Export Citation Format

Share Document