A strongly conservative finite-volume formulation for fluid flows in complex geometries using contravariant velocity components.

摘要

A finite volume formulation of the Navier-Stokes equations is presented in general nonorthogonal curvilinear coordinates. The strong conservation property of the governing equations is retained in discrete form, despite the use of physical contravariant velocity components as dependent variables. This is achieved by means of directly integrating the vector momentum equation over a representative control volume. Following this, the velocity vector is expanded in the set of unit covariant base vectors e;The formulation is tested against a variety of standard test problems, possessing exact or benchmark solutions. A new test problem is proposed in this study, with a view to providing a more stringent evaluation of the robustness of computational schemes. A comparison of the test results with those of some prior formulations indicates that the present formulation performs better, in terms of accuracy as well as order of convergence. The nonstaggered grid approach is shown to outperform the staggered grid approach, even when curvilinear velocity components are used as dependent variables, thereby negating the conventional wisdom that such an advantage was only associated with Cartesian velocity components. Finally, some problems of practical engineering interest featuring flows in irregular geometries are solved. The results indicate that the formulation is capable of providing an enhanced understanding of complex flow phenomena as evidenced by the good agreement of the computations with turbulent flow and heat transfer data for staggered tube banks.