Newton-GMRES Method for Thermal Elasto-hydrodynamic Lubrication of Line Contact Problems

The paper presents, the Newton-GMRES method for the numerical solution of thermal elasto-hydrodynamic lubrication of line contact problem. The viscosity and density of the lubricant are functions of pressure and temperature resulting into a system of equations which are highly nonlinear coupled system of equations. The governing mathematical model includes Reynolds and Energy equations were solved by using second order finite difference method. The computational procedure consists of solving nonlinear system of equations using Newton iteration method for outer loop (nonlinear iteration) and GMRES (Generalized Minimum Residual) method for inner loop (linear iteration). The various physical parameters involved in the present problem are pressure, film thickness with thermal effects of different load and speeds have been discussed in detail. The results obtained are measured with available numerical solutions and are comparable.