Adaptive high-order Discontinuous Galerkin solution of elastohydrodynamic lubrication point contact problems

2012 ◽  
Vol 45 (1) ◽  
pp. 313-324 ◽  
Author(s):  
H. Lu ◽  
M. Berzins ◽  
C.E. Goodyer ◽  
P.K. Jimack
Keyword(s):  
Discontinuous Galerkin ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
High Order ◽  
Galerkin Solution

HIGH-ORDER DISCONTINUOUS GALERKIN SOLUTION OF LOW-RE VISCOUS FLOWS

2009 ◽  
Vol 23 (03) ◽  
pp. 309-312
Author(s):  
HONGQIANG LU
Keyword(s):  
Discontinuous Galerkin ◽  
Euler Method ◽  
High Order ◽  
Navier Stokes ◽  
High Order Schemes ◽  
Seidel Method ◽  
Backward Euler ◽  
Dg Method ◽  
Galerkin Solution ◽  
Nonlinear Discrete System

In this paper, the BR2 high-order Discontinuous Galerkin (DG) method is used to discretize the 2D Navier-Stokes (N-S) equations. The nonlinear discrete system is solved using a Newton method. Both preconditioned GMRES methods and block Gauss-Seidel method can be used to solve the resulting sparse linear system at each nonlinear step in low-order cases. In order to save memory and accelerate the convergence in high-order cases, a linear p-multigrid is developed based on the Taylor basis instead of the GMRES method and the block Gauss-Seidel method. Numerical results indicate that highly accurate solutions can be obtained on very coarse grids when using high order schemes and the linear p-multigrid works well when the implicit backward Euler method is employed to improve the robustness.

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.

Solving EHL Problems Using Iterative, Multigrid, and Homotopy Methods

1999 ◽  
Vol 121 (1) ◽  
pp. 28-33 ◽  
Author(s):  
Elyas Nurgat ◽  
Martin Berzins ◽  
Laurence Scales
Keyword(s):  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Grid Method ◽  
Contact Problems ◽  
Test Problems ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Future Developments ◽  
Relaxation Scheme ◽  
Highly Nonlinear

The numerical solution of ElastoHydrodynamic Lubrication (EHL) point contact problems requires the solution of highly nonlinear systems of equations which pose a formidable computational challenge. Multigrid methods provide one efficient approach. EHL problems solved using a single grid and multigrid will be compared and contrasted with a homotopy method which works on the concept of deforming one problem into another by the continuous variation of a single parameter. Both the multigrid and the single grid method employ a new relaxation scheme. Numerical results on demanding test problems will be used to compare these methods and suggestions for future developments to produce robust solvers will be made.

An Efficient, Robust, Multi-Level Computational Algorithm for Elastohydrodynamic Lubrication

1989 ◽  
Vol 111 (2) ◽  
pp. 193-199 ◽  
Author(s):  
L. Chang ◽  
T. F. Conry ◽  
C. Cusano
Keyword(s):  
Computational Algorithm ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Working Environment ◽  
Ehd Lubrication ◽  
Wide Range ◽  
Direct Iteration ◽  
Multi Level ◽  
And Storage

A new computational algorithm is developed for the numerical analysis of elastohydrodynamic (EHD) lubrication problems. This algorithm combines direct-iteration, Newton-Raphson, and multigrid methods into one working environment. Accurate solutions for a wide range of steady-state, line-contact problems are obtained with a relatively small number of numerical operations. The algorithm can be used to efficiently simulate transient processes in EHD lubrication. It can also be extended to solve point-contact problems with high computational and storage efficiency.

A Generalized Thermal EHL Model for Point Contact Problems

2008 ◽  
Author(s):  
Yuchuan Liu ◽  
Q. Jang Wang ◽  
Dong Zhu ◽  
Fanghui Shi
Keyword(s):  
Surface Temperature ◽  
Thermal Model ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Contact Problems ◽  
Three Dimensions ◽  
Thermal Ehl ◽  
Generalized Reynolds Equation

A generalized thermal elastohydrodynamic lubrication (TEHL) model for point contact problems is developed based on an isothermal generalized Newtonian elastohydrodynamic (EHL) model recently developed. The thermal model couples FDM for lubricant energy equation and the DC-FFT method for surface temperature integration. A generalized Reynolds equation is derived considering the change of viscosity with respect to temperature, pressure and shear in three dimensions. Numerical cases are conducted to verify the model.

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