経済的なエクスプリシット時間差分スキームの開発

Abstract

An economical explicit scheme and its application to a primitive equation model is described. In the present scheme, the low-frequency advection terms are integrated by the leap-frog scheme with a time step interval Δta which is decided by a wind speed of meteorological waves, and not by a gravity wave phase speed. In order to get stable numerical solution, the high frequency gravity wave terms are integrated with a shorter time interval Δtb(≅Δta/M). Time integrations are carried out by combining low frequency terms which are assumed constant during 2Δta leap-frog time extrapolation interval with high frequency terms which are calculated at every Δtb interval. The scheme is three-time-level for low frequency terms. The present scheme is different from the splitting technique proposed by Marchuk (1965).The present economical explicit scheme has the advantage of the easiness in programming and the second order accuracy in the integration of low frequency terms.The present scheme has been applied to the 4L-NHM, operational 4-level northern hemispherical model used in 1978-81 in JMA. The results show that the economical explicit version model produces almost the same prediction as the original (explicit scheme) 4L-NHM. The present scheme saved the computation time as much as the semi-implicit version of 4L-NHM developed by Kudoh (1978) did.