Daubechies Wavelet Multigrid Method for Accurate Solution of Typical Differential Equations Arising in Hydrodynamic Lubrication Theory

Objectives: The present investigation is devoted to analyzing the behavior of pressure and load carrying capacity of the hydrodynamic lubrication problem. The corresponding Reynolds equation of the considered hydrodynamic lubrication problem is acquired by the application of the Stokes equations of motion to the microcontinuum theory. This modification takes into consideration the couple of stress effects that arise from the combination of various additives with the lubricant. Method: The Daubechies wavelet multigrid method is used to find the solution of the non-dimensional Reynolds equation. Findings: Initially to validate the efficiency and accuracy of the proposed strategy, the test problem is considered. The findings of the test problems are presented in tables and captured in terms of the figures to ensure that the proposed method is more accurate and consumes less computational time as compared with the Finite difference method, Multigrid Method. Later, the effect of non-dimensional pressure and load carrying capacity for the considered geometry is calculated for varied parameters. Novelty: Most of the lubrication problems that are available in the literature are solved by the Finite difference method and this Finite difference method has errors (truncation and roundup) and also consumes a lot of time to find the solution. In order to overcome this, the multigrid method was introduced. Again to obtain more accuracy in the solution we used the Daubechies wavelet multigrid method. When a couple stress parameters changes from 0.0 to 0.2 pressure distribution increases to 111.03%. Keywords: Lubrication, Daubechies Wavelet Multigrid Method, Finite Journal Bearing, Couple Stresses, Reynolds Equation