集中豪雨シミュレーションにおける差分スキームについての考察 : その安定性と保存性について

概要

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The author developed a three-dimensional cloud model, and simulated rainstorms. The basic equations for the model contains nine prognostic equations : the Navier-Stokes equations, pressure and thermodynamic equations, three moisture and water equations, and a subgrid kinetic energy equation. Using a terrain-following coordinate transformation, a finite difference scheme solves the model equations. The terms responsible for sound wave generation are integrated on a short time step while a leapfrog marching scheme is performed with the other terms on a large time step. This paper discusses the stability and conservative property of the scheme. First, a weighting coefficient is introduced in integration of the sound terms. A linear stability analysis for this generalized scheme shows that the scheme is most stable when the weighting coefficient is assigned the maximum value. The corresponding scheme is fully implicit in the vertical. Numerical tests confirm its accuracy and stability. Second, some of the prognostic equations are rewritten in the conservative form. A finite difference scheme which has the conservative property is constructed from them and the continuity equation. The scheme improves an unrealistic result obtained by the non-conservative scheme.
日本シミュレーション学会の論文
1987-07-15