A new approach for building bounded skew-upwind schemes Original Research Article

A new methodology for the construction of streamline bounded high resolution schemes is presented. The route followed in the development is to combined existing streamline schemes with the Normalized Variable Formulation (NVF) bounding approach. The procedure is applied to the Skew Upwind Differenting Scheme (SUDS) to yield a new composite high resolution bounded convective scheme (NVF SUDS). The increase in computational cost with NVF SUDS is very small as compared to the unbounded SUDS. The new scheme is tested and compared with the composite high resolution STOIC scheme, the upwind scheme, and the unbounded SUDS by solving for three pure convection test problems. Results generated, demonstrate the capability of the new upwind scheme in accurately resolving steep gradients (as accurate as the ones obtained with the third-order STOIC scheme) while retaining the solution bounded.