特征化积分格式的设计及其在浅水波问题中的应用

The Design of Characterizing-lntegral Schemes and the Application to the Shallow Water Wave Problems

本文介绍一种简单而又行之有效的顺风型格式——特征化积分格式的设计方法及应用技术,用这种方法设计的顺风型格式不受方程有型性的限制,容易推广,又能比较灵活地调节数值耗散性,使之适用不同的间断解的要求.本文利用这种方法作了非线性水波在岸上的变形、破碎过程的数值模拟.结果表明方法稳定、有效;同时作了二维溃坝灾害的数值模拟,表明方法向多维推广的简单、可行性.

In this paper a new approach for desgining upwind type schemes-the charac-terizing-integral method and its applied skills are introduced. The method is simple, convenient and effective. And the method isn't only limited to conservation laws unlike other methods. It maybe easily extended to multi-dimension problems. Furthermore, the numerical dissipation of the method can be flexibly regulated, so that it is especially suitable for solving various discontinuity problems. The paper shows us how to use this approach to s:mulate deformation and breaking of a nonlinear shallow water wave on a gentle slope, and to compute two-dimensional dam failure problem.