JAXA Repository / AIREX 未来へ続く、宙(そら)への英知
Other TitleFormation of shock surfaces over Cartesian grids in numerical computation of scalar conservation laws over two-dimensional space
Author(jpn)相曽, 秀昭
Author(eng)Aiso, Hideaki
Author Affiliation(jpn)宇宙航空研究開発機構航空技術部門数値解析技術研究ユニット(JAXA)
Author Affiliation(eng)Numerical Simulation Research Unit, Aeronautical Technology Directorate, Japan Aerospace Exploration Agency (JAXA)
Issue Date2018-02-22
Japan Aerospace Exploration Agency (JAXA)
Publication title宇宙航空研究開発機構研究開発報告
JAXA Research and Development Report
Start page1
End page9
Publication date2018-02-22
Abstract空間次元が2以上の保存則の解が形成する衝撃波の直交格子による数値計算において、衝撃波面がいずれの格子軸に対しても斜交する場合には格子の方向性の影響で衝撃波に『ギザつき』が生じることが良く知られる。これはまさに数値的な不都合現象であるが、その解析は殆ど行われていない。実際、圧縮性Euler 方程式の場合には複数の要素が入り込み解析は容易ではない。本稿では、スカラー保存則に単純化した問題で解析を行う。解析の結果、『ギザつき』の生成機構については定理の形で明確な記述を得、その不都合の軽減についても考察する。また、この結果は空間1 次元で最適化された差分スキームが多次元では最適とは言えないことも示唆している。
We are concerned with numerical computation of shocks whose surfaces are oblique to any axis of grid for computation, where the grid is a structured orthogonal grid. It is known that the shape of shock surface captured in computation is affected by the computational grid. The shock surface often looks jagged but not smooth even if the shock surface should be planar or smooth from theory. The phenomenon is purely numerical and the machinery of phenomenon is not yet clear. While the setting of problem is rather simple, several different mathematical factors are included and complicatedly related even in the case of compressible Euler equations for ideal gases. Therefore we analyze a simplified problem, scalar conservation laws over the two dimensional space. From the simplified analysis we still discover some essential machinery to form jagged shock surfaces in numerical computation. Finally we obtain a theorem that describes the reason of jaggedness of shock surfaces. It may suggest a method to decrease the inconvenient effect from the grid.
Description形態: カラー図版あり
Physical characteristics: Original contains color illustrations
Keywords衝撃波面の捕獲; スカラー保存則; 空間多次元; 差分近似; Capturing shock surface; Scalar Conservation Law; Multiple space dimension; Difference Approximation
Document TypeTechnical Report
JAXA Category研究開発報告
NASA Subject CategoryFluid Mechanics and Thermodynamics
Report NoJAXA-RR-17-005

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