1次元局所慣性方程式に対する摩擦項を考慮した数値安定性解析  [in Japanese] NUMERICAL STABILITY ANALYSIS OF LOCAL INERTIAL EQUATIONS CONSIDERING THE FRICTION TERM  [in Japanese]

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Abstract

高速な洪水・氾濫計算を実現できる数値モデルの中核として,浅水方程式の慣性項を無視した局所慣性方程式が注目されている.局所慣性方程式を有限差分法によって離散化する場合,摩擦項の半陰的な取り扱いが数値解の安定性を担保し,陽的な取り扱いと比較して許容タイムステップを著しく大きく指定できることが経験的には指摘されてきた.しかし,摩擦項の取り扱いが数値解の安定性に及ぼす影響を理論的に定量化した研究例はない.本研究では,von Neumannの安定性解析を用いて,線形化した摩擦項の取り扱いが空間1次元の局所慣性方程式に対する数値解の安定性に及ぼす影響を定量的に検討した.安定性解析の結果から,摩擦項を陽的に離散化した場合の許容タイムステップが半陰的な場合と比較して著しく小さく,空間ステップが大きい場合に極限値を持つことを示した.また,半陰的な離散化はこの事態を回避できることも示した.さらに,理論的な安定性解析の結果が数値実験の結果と良好に一致することを示した.本研究から,局所慣性方程式に基づく実用的な洪水・氾濫解析において摩擦項の半陰的な取り扱いが果たす役割の重要性が定量的に解明された.

 The local inertial equations, which drop the nonlinear acceleration term from the Saint-Venant equations, are effective and efficient for fast flood computation thanks to its hyperbolic nature and semi-implicit discretization of the friction term. However, mechanisms that the semi-implicit discretization works successfully has not been clarified, which is the motivation of our research. To achieve this, this study applied the von Neumann stability analysis to numerical models of the one-dimensional local inertial equations with explicit, semi-implicit, and implicit discretization of the friction term. The stability analysis led to the exact stability condition for each discretization, and reveals that the semi-implicit discretization enables much larger time step than the explicit counterpart. It was also shown that when the friction term is explicitly discretized, the maximum allowable time step has the upper limitation for coarse spatial resolution. Stability conditions obtained by a series of numerical simulations were in good agreement with the derived stability conditions. The stability analysis of this study revealed the numerical efficiency of the semi-implicit discretization of the friction term in a quantitative manner.

Journal

  • Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering)

    Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering) 73(4), I_577-I_582, 2017

    Japan Society of Civil Engineers

Codes

  • NII Article ID (NAID)
    130006406281
  • NII NACSIS-CAT ID (NCID)
    AN10426673
  • Text Lang
    JPN
  • ISSN
    1880-8751
  • NDL Article ID
    028109583
  • NDL Call No.
    YH247-620
  • Data Source
    NDL  J-STAGE 
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