摘要
WENO方法是在ENO方法的基础上，由Liu,Osher等人于1994年提出的一类新型的高精度、高分辨率格式。WENO格式不但很好的继承了ENO格式的特点，即在间断附近能够保持良好的分辨能力，而且能够引入变化的加权因子，使格式在光滑区解的截断误差阶数又有进一步提高，格式的稳定性又有了进一步的增强。 间断Galerkin方法的深入研究已成为当前数值计算的一个重要方向。由于众多学者的不断发展，间断Galerkin方法在许多方面的应用上显示了前所未有的效能，在解决含有间断现象的问题中发挥着越来越大的作用，广泛地应用到了水动力学、气动力学、波传播等问题。数学上，它在解决椭圆型方程、双曲型守恒律组、对流扩散方程等问题中都是卓有成效的。 本文详细讨论了求解双曲型守恒律方程的两种高精度数值方法，即WENO方法和间断Galerkin方法，并就一些典型问题进行数值比较实验，通过在精度、计算速度和对奇异的分辨率等方面的比较，对这两个方法有了一个较详细的了解，得到了一些有用的结论。
关键词： WENO方法；间断Galerkin方法；高精度方法。
水产品包装设计
赛宾反馈抑制器Abstract
WENO methods is based on the ENO methods by Liu, Osher, who in 1994 proposed a new type of high-precision, high-resolution format. WENO format not only inherits the good features of ENO format, that is interrupted in the vicinity to maintain good resolution capability, but also through the introduction of changes in the weighting factors to form a smooth solution of the truncation error of areas the number had further increased, the format stability, there has been further strengthened.
The research of the discontinuous Galerkin methods has been an important issue of numerical computation. Due to the development of scientists, the discontinuous Galerkin method shows its unprecedented efficiency in many aspects and plays an important part in solving those problems that contain discontinuities. It has widely applied to hydrodynamics, gas dynamics and wave propagation. In mathematics, it is effective in solving elliptic equations, hyperbolic conservation laws and also diffusion equations.
In this paper，we discuss in detail for solving hyperbolic conservation laws equations of two high-precision numerical methods, namely, WENO methods and discontinuous Galerkin methods, and show a number of typical problems numerical comparative tests, by accuracy, computing speed and the resolution of such exotic in comparison, we can get a more detailed understanding of these two methods and obtain some useful conclusions.
Key words: WENO Method;Discontinuous Galerkin Method; High-precision method.
dccik
表目录
表1 WENO方法和间断Galerkin方法求解线性双曲型方程的精度比较 (31)
直言命题表2 WENO方法和间断Galerkin方法CPU时间比较 (34)
周蕾表3 一维激波管问题WENO方法和间断Galerkin方法CPU时间比较 (36)
myie2表4 二维标量方程WENO方法和间断Galerkin方法CPU时间比较 (39)
图目录
图1 Burgers方程光滑初值问题的数值解图 (32)
图2 Burgers方程间断初值问题的数值解图 (33)
图3 Buckley-Leverett问题的数值解图 (34)
图4 Lax问题的密度解示意图 (35)
图5 Sod问题的密度解示意图 (35)
图6 Shu-Osher问题的密度解示意图 (36)
图7 Burgers方程在t=0.2时的示意图 (37)
图8 Burgers方程在t=0.3时的示意图 (38)
图9 Burgers方程在t=0.5时的示意图 (38)
图10 运动波峰问题的示意图。 (39)
豫公网安备41160202000603
站长QQ:729038198
关于我们
投诉建议