101 Application of CIP/Multi-Moment FVM to 2D shallow-water equation on triangular unstructured grids

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  • 101 三角形非構造格子におけるCIP/Multi-Moment FVMの二次元浅水波方程式への適用(OS-1 流体の数値計算法の新しい展開)

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We propose a conservative scheme that suppresses numerical oscillation on triangular unstructured grids. We use "multi-moment" that is one of the features of the CIP method. Three types of so-called "moments", defined as the volume-integrated average (VIA), the point value (PV) and surface-integrated average (SIA) of physical field are used as the prognostic variables to be carried forward in time separately. VIA is updated by a flux formulation, and PV and SIA are updated by a semi-Lagrangian scheme. A 2D quadratic polynomial can be construction over a single triangular element. Numerical oscillation is suppressed by limiting the gradient of a polynomial. Shallow water equation is solved by using Method of Characteristics that is suitable for semi-Lagrangian method. The time-integrated average of flux for updating VIA is approximated by the trajectory-integrated average of Riemann invariant. The proposed method has little numerical oscillation and appears to be robust to different numerical grids by some numerical tests.

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