Stable, non-dissipative, and conservative flux-reconstruction schemes in split forms

Yoshiaki Abe, Issei Morinaka, Takanori Haga, Taku Nonomura, Hisaichi Shibata, Koji Miyaji

研究成果: Article査読

16 被引用数 (Scopus)


A stable, non-dissipative, and conservative flux-reconstruction (FR) scheme is constructed and demonstrated for the compressible Euler and Navier–Stokes equations. A proposed FR framework adopts a split form (also known as the skew-symmetric form) for convective terms. Sufficient conditions to satisfy both the primary conservation (PC) and kinetic energy preservation (KEP) properties are rigorously derived by polynomial-based analysis for a general FR framework. It is found that the split form needs to be expressed in the PC split form or KEP split form to satisfy each property in discrete sense. The PC split form is retrieved from existing general forms (Kennedy and Gruber [33]); in contrast, we have newly introduced the KEP split form as a comprehensive form constituting a KEP scheme in the FR framework. Furthermore, Gauss–Lobatto (GL) solution points and g2 correction function are required to satisfy the KEP property while any correction functions are available for the PC property. The split-form FR framework to satisfy the KEP property, eventually, is similar to the split-form DGSEM–GL method proposed by Gassner [23], but which, in this study, is derived solely by polynomial-based analysis without explicitly using the diagonal-norm SBP property. Based on a series of numerical tests (e.g., Sod shock tube), both the PC and KEP properties have been verified. We have also demonstrated that using a non-dissipative KEP flux, a sixteenth-order (p15) simulation of the viscous Taylor–Green vortex (Re=1,600) is stable and its results are free of unphysical oscillations on relatively coarse mesh (total number of degrees of freedom (DoFs) is 1283).

ジャーナルJournal of Computational Physics
出版ステータスPublished - 2018 1 15

ASJC Scopus subject areas

  • 数値解析
  • モデリングとシミュレーション
  • 物理学および天文学(その他)
  • 物理学および天文学(全般)
  • コンピュータ サイエンスの応用
  • 計算数学
  • 応用数学


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