Newton-Raphson Method for Calculating Line Contact Isothermal Elastohydrodynamic Lubrication

We can employ the Newton-Raphson method to calculate line contact isothermal elastohydrodynamic lubrication and generate pressure and film thickness distribution curves. This method serves as a reliable and widely-used numerical computation approach for simulating and analyzing fluid dynamic phenomena in various engineering environments. The algorithm operates by iteratively solving the Reynolds equation based on fluid parameters including viscosity, density, and velocity to determine pressure and film thickness distributions. The implementation typically involves discretizing the governing equations, establishing proper convergence criteria, and handling boundary conditions through matrix operations. Furthermore, we can validate and refine our computational results using alternative numerical methods and verification tools to ensure accuracy and reliability. Additional validation techniques may include comparing results with analytical solutions, performing grid independence studies, and implementing error analysis procedures to quantify numerical uncertainties.