Wavelet-Multigrid Method for Solving Modified Reynolds Equation Modeling Synovial Fluid Flow in a Normal Human Knee Joint

Abstract

New techniques for numerical solution of partial differential and integral equations, based on the use of multiscale decomposition and wavelet bases, have been proposed. Wavelet-multigrid method, developed recently by the author, is one such scheme for the solution of elliptic partial differential equations, demonstrating the fact that it can be used as a pre-conditioner of the elliptic operator as well as a fast solver.

The low frictional force and negligible wear in the synovial joint is a well-observed phenomenon. Many attempts have been made to explain the experimental results by the current lubrication theories. The main purpose of this chapter is to study effects of surface roughness and poroelasticity on the squeeze film behavior of bearings in general and that of synovial joints in particular. Modified Reynolds equation, which models the lubrication phenomenon in a normal human knee joint, has been solved using wavelet-multigrid method. The numerical results obtained can be used to select suitable design parameters, as a result of which, the bearing performance can be improved. They also serve as a clinical tool and might turn out to be highly appropriate for the diagnosis of degenerative joint disease.