ENTROPY VISCOSITY FOR CONSERVATION EQUATIONS
ENTROPY VISCOSITY FOR CONSERVATION EQUATIONS
复制标题
守恒方程的熵粘度
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
B. Popov
中科院分区：
文献类型：
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作者：
J. Guermond;R. Pasquetti;B. Popov
我们提出了一个“熵粘性方法”的近似守恒律和更一般的守恒方程或系统，可能会表现出非光滑的解决方案。为了强调其功能，我们专注于一些非平凡的问题，由非线性标量守恒律或可压缩欧拉方程。用有限元、傅立叶谱法和谱元得到的数值结果表明，可以使用不同类型的近似。我们还考虑了线性标量平流方程，我们解决了谱元素，提供了一个数值证据，基本方法的准确性是保留。这种稳定化方法是基于在控制方程中引入非线性稳定化项，该非线性稳定化项利用与所考虑的问题相关联的熵方程的残差构造的非线性粘度。
We present an “entropy viscosity method” for the approximation of conservation laws and more generally of conservation equations or systems that may exhibit nonsmooth solutions. To emphasize its capabilities we focus on some non-trivial problems, governed by non-linear scalar conservation laws or by the compressible Euler equations. Numerical results obtained with finite elements, Fourier spectal method and spectral elements are provided to outline the fact that different types of approximations may be used. We also consider the linear scalar advection equation, that we solve with spectral elements, to provide a numerical evidence that the accuracy of the underlying method is preserved. This stabilization method is based on the introduction in the governing equations of a non-linear stabilizing term, which makes use of a non-linear viscosity constructed from the residual of the entropy equation associated to the considered problem.