A novel weighting switch function for uniformly high‐order hybrid shock‐capturing schemes. (10th August 2016)

• Record Type: Journal Article
• Authors: Peng, Jun; Shen, Yiqing
• Is Part Of: International journal for numerical methods in fluids. Volume 83:Number 9(2017)
• Page Start: 681
• Page End: 703
• Publication Date: 2016-08-10
• Subjects: WENO scheme -- switch function -- hybrid scheme -- compressible flow; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4285
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: Hybrid schemes are very efficient for complex compressible flow simulation. However, for most existing hybrid schemes in literature, empirical problem‐dependent parameters are always needed to detect shock waves and hence greatly decrease the robustness and accuracy of the hybrid scheme. In this paper, based on the nonlinear weights of the weighted essentially non‐oscillatory (WENO) scheme, a novel weighting switch function is proposed. This function approaches 1 with high‐order accuracy in smooth regions and 0 near discontinuities. Then, with the new weighting switch function, a seventh‐order hybrid compact‐reconstruction WENO scheme (HCCS) is developed. The new hybrid scheme uses the same stencil as the fifth‐order WENO scheme, and it has seventh‐order accuracy in smooth regions even at critical points. Numerical tests are presented to demonstrate the accuracy and robustness of both the switch function and HCCS. Comparisons also reveal that HCCS has lower dissipation and less computational cost than the seventh‐order WENO scheme. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : In this paper, a parameter‐free weighting switch function is proposed for developing a family of high order hybrid schemes. As an example, a seventh‐order hybrid compact‐CRWENO scheme (HCCS) is constructed and analyzed with the proposed function. Numerical results show that the new scheme has very low dissipation and maintains the essentially non‐oscillation property of the base‐CRWENO scheme. As shown in this figure, HCCS is even more efficient than the seventh‐order WENO scheme.