A NEW HIGH-RESOLUTION SCHEME BASED ON THE NORMALIZED VARIABLE FORMULATION

Abstract

A high-resolution (HR) discretization scheme is proposed for the calculation of incompressible steady-state convective flow with finite-volume methods. The basic algorithm combines a second- and third-order interpolation profile applied in the context of the normalized variable formulation (NVF). The new scheme is tested by solving three problems: (1) a two-dimensional pure convection of a scalar involving a step profile in an oblique velocity field; (2) a two-dimensional pure convection of a scalar involving an elliptic profile in an oblique velocity field; (3) the Smith-Hutton [1] problem involving pure convection of a step profile in a rotational velocity field. The computational results obtained are compared with the results of six HR schemes: Leonard's EVLER scheme, Gaskell and Lau's SMART scheme, Van Leer's CLAM and MUSCL schemes, Chakravarthy and Osher's OSHLR scheme, Roe's M1NMOD scheme, and the exact solution. The results for the new scheme, STOIC demonstrate its capability in capturing steep gradients while maintaining the boundedness of solutions. Furthermore, the comparison with other HR schemes shows that the STOIC scheme yields the most accurate results without undue physical oscillations or numerical smearing