双曲守恒律方程的降阶Spectral Volume方法研究

摘要

The notion of reduced-order spectral volume method(SVM)is proposed.Formulation of the reduced-order SVM is studied. New method is applied to one-dimensional scalar conservation law.The diffusion and dispersion property of reduced-order SVM is studied by using Fourier analysis.Comparison shows that the reduced-order SVM has an advantage in terms of diffusion and dispersion property over the traditional SVM.%文章中提出了降阶的Spectral Volume 方法(SV方法)的概念，对方法的公式进行推导，并成功将其应用与一维线性传递方程。对降阶的SV方法的稳定性进行了Fourier分析，并与传统的SV方法进行了对比。实验证明，降阶的SV方法在初值连续情况下，在线性传递方程上可以达到所期望的数值精度，并且在数值色散和数值耗散特性上较传统SV方法有显著提高。