A sensitivity study of relaxation parameter in Uzawa algorithm for the steady natural convection model

Abstract

Purpose This paper aims to study the sensitivity of relaxation parameter in Uzawa method for the steady natural convection model. Design/methodology/approach Based on the continuous sensitivity equation method, associated sensitivity system is formed, which is solved by applying finite element method. Findings A decrease in sensitivity values of velocity, pressure and temperature is observed as the relaxation parameter increases. Originality/value The sensitivity study of relaxation parameter in Uzawa method is the first for the natural convection model, to the best of the authors’ knowledge. In fact, it is difficult to find an optimal relaxation parameter in the Uzawa method for the nonlinear problems. It is therefore important to understand how small changes in the relaxation parameter could affect the numerical solution of the nonlinear equations.