The expanded upwind-mixed multi-step method for the miscible displacement problem in three dimensions

2008 ◽  
Vol 195 (1) ◽  
pp. 100-109 ◽  
Author(s):  
Huailing Song ◽  
Yirang Yuan
Keyword(s):  
Miscible Displacement ◽  
Three Dimensions ◽  
Step Method ◽  
Displacement Problem

Three-Dimensional Analysis of Knee Joint Movement with Biplanar Photography, with Special Reference to the Analysis of ‘dynamic’ Knee Instabilities

1993 ◽  
Vol 207 (3) ◽  
pp. 163-173 ◽  
Author(s):  
H Matsumoto ◽  
B B Seedhom
Keyword(s):  
Knee Joint ◽  
Pivot Shift ◽  
Three Dimensional ◽  
Sufficient Accuracy ◽  
Three Dimensions ◽  
Joint Movement ◽  
Step Method ◽  
Actual Measurement ◽  
Knee Movement ◽  
Cadaveric Knee

An apparatus was developed by means of which it was possible to move a cadaveric knee joint under a constant external force and to measure its movement in three dimensions using biplanar photography, to investigate mechanisms of ‘dynamic’ knee instabilities, such as the ‘pivot shift’ phenomenon. Two wire frameworks, one attached to the femur, the other to the tibia, defined a system of three mutually orthogonal axes. While the knee joint was moved under a given force, a series of biplanar photographs of the two frameworks were taken. This procedure was repeated after sectioning different ligaments simulating different injuries. The joint was finally fully disarticulated, but leaving the reference wire frameworks still attached to their respective bone. Another series of biplanar photographs of the femur and tibia were taken. From these two series of measurements, movements of the tibia with respect to the femur were calculated. With this two-step method, knee movements could be measured without damaging the knee structures before or during the actual measurement (which could change the knee movement itself). On validating the system, it was concluded that knee movement could be measured with sufficient accuracy for the analysis of knee instability.

scholarly journals Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem

2018 ◽  
Vol 19 (2) ◽  
pp. 333-374 ◽  
Author(s):  
Jérôme Droniou ◽  
Robert Eymard ◽  
Alain Prignet ◽  
Kyle S. Talbot
Keyword(s):  
Convergence Analysis ◽  
Miscible Displacement ◽  
Numerical Schemes ◽  
Displacement Problem
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