scholarly journals High-Order Finite-Difference Method for Incompressible Flows Using Collocated Grid System.

1998 ◽  
Vol 41 (4) ◽  
pp. 830-839 ◽  
Author(s):  
Takeo KAJISHIMA ◽  
Takashi OHTA ◽  
Kazuhiko OKAZAKI ◽  
Yutaka MIYAKE
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Incompressible Flows ◽  
High Order ◽  
Grid System ◽  
Collocated Grid ◽  
High Order Finite Difference

Fully Coupled Numerical Methods for Elastohydrodynamic Lubrication Line Contact Problems by the High Order Finite Difference Methods

2021 ◽  
Author(s):  
QUAN SHEN ◽  
Bing Wu ◽  
GUANGWEN XIAO
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Scheme ◽  
Difference Method ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
High Order ◽  
Line Contact ◽  
High Order Finite Difference ◽  
Upwind Finite Difference

Abstract In this paper a high order finite difference method is constructed to solve the elastohydrodynamic lubrication line contact problems, whose cavitation condition is handled by the penalty method. The highly nonlinear equations from the discretization of the high order finite difference method are solved by the trust-region dogleg algorithm. In order to reduce the numerical dissipation and dispersion brought by the high order upwind finite difference scheme, a high order biased upwind finite difference scheme is also presented. Our method is found to achieve more accurate solutions using just a small number of nodes compared to the multilevel methods combined with the lower order finite difference method.

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