B-EXPRESS: A new bounded extremum-preserving strategy for convective schemes

The indiscriminate application of the convective boundedness criterion (CBC ) in all flow regions results in a new and subtle error that leads to a sig nificant reduction in accuracy at locations where physical extrema (maxima or minima),vith sleep profiles are present. In this article, a new Bounded EXtremum-PREServing Strategy (B-EXPRESS) that addresses this issue is prese nted. The B-EXPRESS is a two-stage procedure in which an extremum recogniti on 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 locat ions, 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 proble ms 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% mor e CPU time than the B-EXPRESS-3 scheme. Moreover, the B-EXPRESS-7 scheme co mputations do not show any observable attenuation in the levels of the prof iles while marginally increasing the CPU effort (3.43% on average) over the BSEVENTH scheme.