A p -version finite element gas bearing program for pivoted calculations based on false transient response

Abstract An efficient finite element program for pivoted gas bearing design calculations, called p -GAS, is presented. The program is constructed based on the modified, steady-state, compressible lubrication Reynolds equation and static equilibrium equations. p -GAS provides pivoted solutions by tracking false transient responses. The present gas bearing finite element program yields accurate numerical solutions. It conveniently provides higher-order solutions since this program utilizes a hierarchical finite element formulation, and it requires less computing time than does even the most efficient known-to-date factored implicit finite difference scheme. The success of p -GAS rests on three factors, namely, the hierarchical p -version finite element method, which reduces the total degrees of freedom needed for modeling the bearing systems; the artificial transient approach which rapidly brings the bearing attitude to the correct attitude; and the Gaussian frontal solver which accelerates the matrix solving time by reducing the in-core storage requirement. Experiments with reduced integrations, which save the computing effort, yield acceptable results. Directions on further reduction of the computations are briefly discussed.