Hybrid high-order steepness-adjustable harmonic scheme based on combined discontinuity sensors. (15th June 2022) - Ruan, Yucang; Tian, Baolin; Zhang, Xinting; He, Zhiwei
Highlights: The conception of combined discontinuity sensors and hybrid schemes of high-resolution schemes and discontinuity-preserving scheme. A specific hybrid fourth-degree linear polynomial steepness adjustable harmonic scheme based on combined monotonicity-preserving weighted group-velocity controlled discontinuity sensors. An evaluation of nine usual single discontinuity sensors. Abstract: Extending discontinuity-capturing schemes to high resolution using a hybrid approach has become popular in recent times. The hybrid schemes reported in literature usually combine high-order compact/explicit-schemes in smooth regions and the weighted essentially non-oscillatory (WENO) scheme in discontinuities by a discontinuity sensor. However, there are two major concerns: (1) the significant dissipation of the WENO scheme will smear the contact discontinuities, and (2) the accuracy of the discontinuity sensor will significantly influence the performance of the hybrid scheme. However, these two aspects are typically coupled. Therefore, in this study, we attempt to replace the discontinuity-capturing schemes (WENO) with discontinuity-preserving schemes (steepness-adjustable harmonic (SAH) scheme). Then, we extend the SAH scheme to high-order accuracy by hybridizing it with a linear fourth-degree polynomial (P4) scheme. The new P4-SAH scheme was employed to evaluate the nine different discontinuity sensors. The numerical results revealed that a single discontinuity sensor can hardly adapt to different numerical cases. Therefore, we propose a new class of discontinuity sensors that combines MP-WGVC discontinuity sensors. Several classical one- and two-dimensional Euler equation benchmark tests were simulated. The numerical results demonstrate that the new hybrid P4-SAH scheme with a combined MP-WGVC sensor not only sharply captures shock waves and contact discontinuities, but also capture small vortex structures.