Element length calculation in B-spline meshes for complex geometries

Yuto Otoguro, Kenji Takizawa*, Tayfun E. Tezduyar


研究成果: Article査読

26 被引用数 (Scopus)


Variational multiscale methods, and their precursors, stabilized methods, have been playing a core-method role in semi-discrete and space–time (ST) flow computations for decades. These methods are sometimes supplemented with discontinuity-capturing (DC) methods. The stabilization and DC parameters embedded in most of these methods play a significant role. Various well-performing stabilization and DC parameters have been introduced in both the semi-discrete and ST contexts. The parameters almost always involve some element length expressions, most of the time in specific directions, such as the direction of the flow or solution gradient. Until recently, stabilization and DC parameters originally intended for finite element discretization were being used also for isogeometric discretization. Recently, element lengths and stabilization and DC parameters targeting isogeometric discretization were introduced for ST and semi-discrete computations, and these expressions are also applicable to finite element discretization. The key stages of deriving the direction-dependent element length expression were mapping the direction vector from the physical (ST or space-only) element to the parent element in the parametric space, accounting for the discretization spacing along each of the parametric coordinates, and mapping what has been obtained back to the physical element. Targeting B-spline meshes for complex geometries, we introduce here new element length expressions, which are outcome of a clear and convincing derivation and more suitable for element-level evaluation. The new expressions are based on a preferred parametric space and a transformation tensor that represents the relationship between the integration and preferred parametric spaces. The test computations we present for advection-dominated cases, including 2D computations with complex meshes, show that the proposed element length expressions result in good solution profiles.

ジャーナルComputational Mechanics
出版ステータスPublished - 2020 4月 1

ASJC Scopus subject areas

  • 計算力学
  • 海洋工学
  • 機械工学
  • 計算理論と計算数学
  • 計算数学
  • 応用数学


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