B-EXPRESS: A NEW BOUNDED EXTREMUM-PRESERVING STRATEGY FOR CONVECTIVE SCHEMES

Abstract

The indiscriminate application of the convective boundedness criterion (CBC) in all flow regions results in a new and subtle error that leads to a significant reduction in accuracy at locations where physical extrema (maxima or minima) with steep profiles are present. In this article, a new Bounded EXtremum-PREServing Strategy (B-EXPRESS) that addresses this issue is presented. The B-EXPRESS is a two-stage procedure in which an extremum recognition algorithm (ERA) is first applied to a solution converged to a set level to flag locations at which enforcing the CBC leads to extrema attenuation. Then, in the second stage, an unbounded scheme is used at the flagged locations, while a bounded scheme is used elsewhere. The new strategy is applied to the SMART (a third-order-bounded scheme) and BSEVENTH (a seventh-order-bounded scheme) schemes to yield two new schemes denoted by B-EXPRESS-3 and B-EXPRESS-7, respectively. These schemes are tested by solving four problems of pure convection in an oblique velocity field of sinusoidal, elliptic, triangular, and box profiles. Results obtained reveal that the B-EXPRESS-3 greatly reduces the rate of attenuation in the levels of the profiles and is as accurate as the BSEVENTH scheme, which, on average, requires 540% more CPU time than the B-EXPRESS-3 scheme. Moreover, the B-EXPRESS-7 scheme computations do not show any observable attenuation in the levels of the profiles while marginally increasing the CPU effort (3.43% on average) over the BSEVENTH scheme.