求解正则长波方程的一种基于NV/TVD的 高分辨率有限体积格式
A High Resolution NV/TVD Finite Volume Scheme for the Regularized Long Wave Equation

作者: 高 巍 , 睢国钦 , 李 宏 :内蒙古大学数学科学学院,呼和浩特;

关键词: 正则长波方程TVDCBC有限体积方法Regularized Long Wave Equation TVD CBC Finite Volume

摘要:

本文构造了一种求解正则长波方程的高分辨率高阶有限体积格式,它以QUICK有限体积格式作为基础格式,以期在光滑解区域获得数值高精度。另外,它结合TVD和CBC两种对流有界准则来抑制数值解的非物理振荡。几个典型的算例表明,本文提出的数值格式保持了有限体积方法良好的守恒性,同时又具有高精度和良好的计算稳定性。

An oscillation-free high order scheme is presented for regularized long wave equations by using the normalized-variable formulation in the finite volume framework. It adopts the QUICK finite volume scheme as the basic scheme to obtain high order accuracy in smooth solution domain. In order to suppress unphysical oscillations of numerical solutions by high order linear schemes, the CBC (convection boundness criterion) condition is combined with the TVD (total variation diminishing) constraint to design a bounded QUICK scheme. Numerical results demonstrate that the present scheme possesses good robustness and high resolution.

文章引用: 高 巍 , 睢国钦 , 李 宏 (2014) 求解正则长波方程的一种基于NV/TVD的 高分辨率有限体积格式 。 流体动力学, 2, 1-11. doi: 10.12677/IJFD.2014.21001

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