双曲型守恒律方程的无振荡谱体积方法
An Oscillation-free Spectral Volume Method for Hyperbolic Conservation Laws
摘要：
本文提出并研究了双曲型守恒律方程的无振荡谱体积（OFSV）方法。数值格式的设计是通过在标准谱体积法中引入阻尼项来控制间断附近的寄生振荡。在构造控制体的基础上，提出了两类OFSV格式。给出了一个数学证明，证明了所提出的OFSV算法是稳定的，并具有最优的收敛速度和超收敛性.理论分析和数值实验都表明，阻尼项的引入不会破坏原SV格式的精度，并能有效地控制振荡的不连续性。数值实验证明了我们的计划的准确性和鲁棒性。
英文摘要：
In this paper, an oscillation-free spectral volume (OFSV) method is proposed and studied for the hyperbolic conservation laws. The numerical scheme is designed by introducing a damping term in the standard spectral volume method for the purpose of controlling spurious oscillations near discontinuities. Based on the construction of control volumes (CVs), two classes of OFSV schemes are presented. A mathematical proof is provided to show that the proposed OFSV is stable and has optimal convergence rate and some desired superconvergence properties when applied to the linear scalar equations. Both analysis and numerical experiments indicate that the damping term would not destroy the order of accuracy of the original SV scheme and can control the oscillations discontinuities effectively. Numerical experiments are presented to demonstrate the accuracy and robustness of our scheme.
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