An implicit method using contravariant velocity components and its application to calculations in a harbour-channel area  

作　　者：Shi Fengyan, Kong Yazhen and Ding Pingxing (State Key Laboratory of Estuarine and Coastal Research, East China Normal University. Shanghai 200062, China) 

出　　处：《Acta Oceanologica Sinica》1998年第4期423-432,共10页海洋学报（英文版）

摘　　要：The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity. To solve this problem, implicit schemes should be adopted since explicit schemes may bring about a great increase in computation quantity according to the Courant-FrledrichsLewy condition. Whereas the adoption of implicit schemes is difficult to be realized because of the existence of two partial derivatives of surface elevations with respect to variables of alternative direction coordinates in each momentum equation in non-rectangular coordinates. With an aim to design an implicit scheme in non-reetangular ccordinates in the present paper, new momentum equations with the contravariant components of velocity vector are derived based on the shallow water dynamic equations in generalized curvilinear coordinates. In each equation, the coefficients before the two detivatives of surface elevations have different orders of magnitude, i. e., the derivative with the larger ceefficient rnay play a more important role than that with the smaller one. With this advantage, the ADI scheme can then be easily employed to improve the numerical stability and decrease the calculating quantity. The calculation in a harbour and a channel in Macau nearshore area shows that the implicit model is effective in calculating current fields in small size areas.The key problem in the computation of fluid dynamics using fine boundary-fitted grids is how to improve the numerical stability and decrease the calculating quantity. To solve this problem, implicit schemes should be adopted since explicit schemes may bring about a great increase in computation quantity according to the Courant-FrledrichsLewy condition. Whereas the adoption of implicit schemes is difficult to be realized because of the existence of two partial derivatives of surface elevations with respect to variables of alternative direction coordinates in each momentum equation in non-rectangular coordinates. With an aim to design an implicit scheme in non-reetangular ccordinates in the present paper, new momentum equations with the contravariant components of velocity vector are derived based on the shallow water dynamic equations in generalized curvilinear coordinates. In each equation, the coefficients before the two detivatives of surface elevations have different orders of magnitude, i. e., the derivative with the larger ceefficient rnay play a more important role than that with the smaller one. With this advantage, the ADI scheme can then be easily employed to improve the numerical stability and decrease the calculating quantity. The calculation in a harbour and a channel in Macao nearshore area shows that the implicit model is effective in calculating current fields in small size areas.

关 键 词：Numerical model contravariant component of velocity vector implicit scheme 

分 类 号：P731.2[天文地球—海洋科学]