Weighted Least-squares Cell-Average Gradient Construction Methods For The VULCAN-CFD Second-Order Accurate Unstructured Grid Cell-Centered Finite-Volume Solver

2019 ◽  
Author(s):  
Jeffery A. White ◽  
Hiroaki Nishikawa ◽  
Robert A. Baurle
Keyword(s):  
Least Squares ◽  
Finite Volume ◽  
Unstructured Grid ◽  
Weighted Least Squares ◽  
Grid Cell ◽  
Second Order ◽  
Average Gradient ◽  
Construction Methods ◽  
Cell Average

Determination of First and Second Order Instant Screw Parameters from Landmark Trajectories

1992 ◽  
Vol 114 (2) ◽  
pp. 274-282 ◽  
Author(s):  
H. J. Sommer
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Angular Acceleration ◽  
Second Order ◽  
The Body ◽  
Least Squares Estimators ◽  
Linear Relationships ◽  
Count Distribution ◽  
Body Velocity ◽  
Instant Screw Axis

Least squares methods were developed to determine instant screw axis (ISA) and angular acceleration axis (AAA) parameters in experimental and analytical studies. The algorithms provide linear relationships for rigid body velocity and acceleration descriptors based on position, velocity, and acceleration data for individual points on the body. Weighted least squares estimators are presented for statistical weighting on individual landmarks as well as for variance weighting to reduce systematic measurement effects. The methods include instantaneous second order screw motion which describes differential geometry of screw axodes. Two spatial mechanism examples provide recommendations for landmark count, distribution, and placement.

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