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

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.

Sensitivity Analysis and Computations of the Time Relaxation Model

This paper presents a numerical study of the sensitivity of a fluid model known as time relaxation model with respect to variations of the time relaxation coefficientχ. The sensitivity analysis of this model is utilized by the sensitivity equation method and uses the finite element method along with Crank Nicolson method in the fully discretization of the partial differential equations. We present a test case in support of the sensitivity convergence and also provide a numerical comparison between two different strategies of computing the sensitivity, sensitivity equation method and forward finite differences.

Inverse Problem for Looped River Networks – Lower oder River Case Study

Identification of coefficients determining flow resistance, in particular Manning’s roughness coefficients, is one of the possible inverse problems of mathematical modeling of flow distribution in looped river networks. The paper presents the solution of this problem for the lower Oder River network consisting of 78 branches connected by 62 nodes. Using results of six sets of flow measurements at particular network branches it was demonstrated that the application of iterative algorithm for roughness coefficients identification on the basis of the sensitivity-equation method leads to the explicit solution for all network branches, independent from initial values of identified coefficients.