The performance of newton-raphson linearization in collocated schemes

摘要

Introducing a dual-definition for the velocity component at control surfaces is a general strategy which leaves a number of ambiguities concerning the nonlinear terms of the governing equations. This investigation shows that there will be great improvement in the performance of a control volume algorithm if a correct and conceptual linearization strategy is considered. In this work, a detailed study is performed for unsteady compressible flow with uniform temperature in order to quantify the performance of an improved collocated scheme in the absence of the energy equation. It is shown that the performance of the algorithm which employs conceptual linearization improves if the energy equation is decoupled from the set of governing equations.