A NEW FAMILY OF STREAMLINE-BASED VERY-HIGH-RESOLUTION SCHEMES

Abstract

A number of high-resolution (HR) schemes are reformulated in streamline-based coordinates and bounded using the convection boundedness criterion (CBC) in the context of the normalized variable and space formulation methodology (NVSF). This new approach yields a family of very-high-resolution (VHR) schemes that combines the advantages of the traditional HR schemes with the multidimensional nature of streamline-based schemes. The resultant VHR schemes, which are based on the MINMOD, OSHER, MUSCL, CLAM, SMART, STOIC, EXPONENTIAL, and SUPER-C HR schemes, are tested and compared with their base HR schemes by solving four problems: (1) pure convection of a step profile in an oblique velocity field; (2) sudden expansion of an oblique velocity field in a rectangular cavity; (3) driven flow in a skew cavity; and (4) gradual expansion in an axisymmetric, nonorthogonal channel. Results reveal that the new schemes are bounded and are by far more accurate than the original HR schemes in situations when the flow is highly skew to the grid lines.