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.
翻译:在本文中,为双曲线保护法提出并研究了无振荡光谱体积法(OFSV)方法,该数字方法的设计是在标准光谱体积法中引入一个标记术语,以控制接近不连续的虚假振荡。根据控制量的构造,提出了两种类别FOSV方案。提供了数学证据,以证明拟议的紫外线光谱体积稳定,并具有最佳趋同率和某些理想的超趋同性能。分析和数字实验都表明,标记词不会破坏原SV方案的准确性,而且能够有效控制振荡不连续。做了数字实验,以证明我们的计划准确性和稳健性。</s>