Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition (Communications in Computational Physics, 2023)
In this paper, we present a hybrid form of weighted compact nonlinearscheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinearmethods for smooth and discontinuous zones individually. To fulfill this algorithm,it is inseparable from the recognition ability of the discontinuity detector adopted. Inspecific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shockwaves and contact discontinuities, while avoiding misjudgments of smooth structures.Some classical detectors are classified into three basic types: derivative combination,smoothness indicators and characteristic decomposition. Meanwhile, a new improveddetector is proposed for comparison. Then they are analyzed through identifying aseries of waveforms firstly. After that, hybrid schemes using such indicators, as wellas different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulationresults demonstrate that the proposed algorithm has similar performances to pureWCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40percent for 2D Euler equations. Current research is in the hope of providing somereference and establishing some standards for judging existing discontinuity detectorsand developing novel ones.