An optimized dispersion-relation-preserving combined compact difference scheme to solve advection equations

• Published in: arXiv.org
• Main Authors: Ching-Hao, Yu, Wang, Dan, He, Zhiguo, Pähtz, Thomas
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 12.08.2015
• Subjects: Advection; Anisotropy; Dispersion; Mathematical analysis; Phase velocity; Physics - Computational Physics; Physics - Fluid Dynamics; Stability analysis
• DOI: 10.48550/arxiv.1508.02830

In this study, we first present an improved version of the classical sixth-order combined compact difference (CCD6) scheme to enhance the convective stability of advection equations through an increased dispersion accuracy. This improved fifth-order dispersion-relation-preserving combined compact difference scheme (DRPCCD5) has been rigorously analyzed through the dispersion, phase speed anisotropy and stability analyses. We then couple the DRPCCD5 scheme with the previous fifth-order compact-reconstruction weighted essentially non-oscillatory (CRWENO5) scheme using a novel hybrid strategy based on the monotonicity-maintenance criteria. To verify the resulting "optimized" hybrid scheme (ODRPCCD5), several benchmark problems with available exact solution are investigated. The comparison to the previous fifth-order WENO (WENO5) scheme shows that the ODRPCCD5 avoids numerical oscillation around discontinuities, handles large gradients well, and is much faster at the same accuracy because a coarser mesh can be used.