论文标题
可压缩Navier-Stokes系统的惩罚有限体积方法的收敛性和错误估计
Convergence and error estimates of a penalization finite volume method for the compressible Navier-Stokes system
论文作者
论文摘要
在数值模拟中，流体占据的平滑域必须由通常与物理域不一致的计算域近似。因此，为了研究数值方法域与离散误差的收敛性和误差估计，需要考虑所谓的变异犯罪。在本文中，我们通过惩罚方法提出了一种直接但技术性分析的优雅替代方案。我们将物理结构域嵌入到足够大的立方体结构域中，并研究有限体积方法的收敛性，以解决相应的域含量问题。我们表明，被刑罚问题的数值解决方案将原始问题的所谓耗散弱解决方案融合到了普遍的，所谓的耗散弱解决方案。如果存在强溶液，则从相同的初始数据发出的耗散弱解与强溶液一致。在这种情况下，我们应用了相对能量的新工具，并得出数值解决方案和强溶液之间的误差估计。提出了确认理论结果的广泛数值实验。
In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we present an elegant alternative to a direct, but rather technical, analysis of variational crimes by means of the penalty approach. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.
