An efficient very-high-resolution scheme based on an adaptive-scheme strategy

A new, efficient, adaptive very-high-resolution (AVHR) scheme based on the normalized variable and space formulation methodology is presented in this article. The scheme is composed of the high-resolution SMART scheme and a wide stencil scheme based on a bounded seventh-order interpolation profile denoted here by BSEVENTH. The normalized weighting factor (NWF) acceleration technique and the deferred-correction procedure are used to implement the SMART and BSEVENTH schemes, respectively. The AVHR scheme switches to the seventh-order profile near a discontinuity or in the presence of a high gradient and to the SMART scheme in smooth regions. A new normalized switching criterion is developed, and its accuracy is illustrated for a number of scalar profiles. Numerical results for four purely convective lest problems show that while if preserves the accuracy of the BSEVENTH scheme, the new AVHR scheme reduces the cost by more than 400%, if compared to the traditional DC implementation of the BSEVENTH scheme and by 50% when compared to a new accelerated NWF-DC implementation of the BSEVENTH scheme.