High-Order Low-Dissipation Shock-Resolving TENO-THINC Schemes for Hyperbolic Conservation Laws  

作　　者：Shinichi Takagi Hiro Wakimura Lin Fu Feng Xiao 

机构地区：[1]Department of Mechanical Engineering,Tokyo Institute of Technology,2-12-1 Ookayama Meguro-ku,Tokyo,152-8550,Japan [2]Department of Mechanical and Aerospace Engineering,The Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong,China [3]Department of Mathematics,The Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong,China [4]HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute,Futian,Shenzhen,China [5]Shenzhen Research Institute,The Hong Kong University of Science and Technology,Shenzhen,China

出　　处：《Communications in Computational Physics》2023年第9期1043-1078,共36页计算物理通讯（英文）

基　　金：supported by National Key R&D Program of China(No.2022YFA1004500);Lin Fu acknowledges the fund from the Research Grants Council(RGC)of the Government of Hong Kong Special Administrative Region(HKSAR)with RGC/ECS Project(No.26200222);the fund from Guangdong Basic and Applied Basic Research Foundation(No.2022A1515011779);the fund from Key Laboratory of Computational Aerodynamics,AVIC Aerodynamics Research Institute,and the fund from the Project of Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone(No.HZQB-KCZYB-2020083);Feng Xiao acknowledges the fund from JSPS(Japan Society for the Promotion of Science)under Grant Nos.18H01366 and 19H05613;Hiro Wakimura acknowledges the fund from JSPS under Grant No.22KJ1331.

摘　　要：While the recently proposed TENO(targeted essentially non-oscillatory)schemes[Fu et al.,Journal of Computational Physics 305(2016):333-359]exhibit better performance than the classical WENO(weighted essentially non-oscillatory)schemes with the same accuracy order,there is still a room for further improvement,e.g.,the physical discontinuities may be significantly smeared by the excessive numerical dissipation due to the enforcement of the ENO property after a long-time advection.More recently,a new fifth-order TENO5-THINC scheme is proposed by coupling the TENO5 scheme with a non-polynomial THINC(tangent of hyperbola for interface capturing)scheme based on a parameter-free discontinuity indicator.The novelty originates from the fact that the new strategy locates the discontinuities accurately and deploys the jump-like THINC reconstruction scheme for resolving the discontinuities with a sub-cell resolution,instead of enforcing the ENO property.The new scheme successfully leverages the excellent wave-resolution property of standard TENO schemes for smooth and under-resolved continuous scales and the discontinuity-resolving capability of THINC for reconstructing genuine discontinuities.In this work,we further develop the low-dissipation discontinuity-resolving very-high-order TENO-THINC reconstruction schemes for hyperbolic conservation laws by proposing tailored coupling strategies.Without loss of generality,the six-and eight-point TENO-THINC schemes are developed,and the explicit formulas are given as well as the built-in parameters.Based on a set of critical benchmark simulations,the newly proposed schemes show S.Takagi,H.Wakimura,L.Fu and F.Xiao/Commun.Comput.Phys.,34(2023),pp.1043-1078 significantly lower numerical dissipation when compared to the counterpart TENO schemes without sacrificing numerical robustness.The presented numerical results represent the state-of-the-art in the literature and can serve as references for future algorithm development.

关 键 词：TENO THINC WENO high-order numerical schemes low-dissipation schemes compressible flows 

分 类 号：O17[理学—数学]