Computation methods for hydrodynamic problems (Reynold's equation)

This paper deals with the application of numerical methods to finding approximate solutions for a two-dimensional Reynolds' equation.Pressure height parameters ($\text{P}{}^1$) are evaluated at a series of discrete points on a rectangular mesh in the circumferential direction. Using these parameters the Reynold's equation is transformed into its equivalent finite difference form.In this form the equation gives the value of the pressure height parameter $\text{P}{}^1$ in terms of the values at neighbouring points and the corresponding influence coefficients. The finite difference equation is solved using an interactive method.Jacobi, Gauss-Seidel and successive over-relaxation methods are discussed. It is observed that by using an optimum over-relaxation factor, much computer time can be saved. Finally a convergence criterion is discussed which decides the iteration process.