Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux
Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux
复制标题
DOI：
10.1016/0021-9991(87)90074-x
复制
发表时间：
1985-12
影响因子：
4.1
通讯作者：
W. F. Noh
中科院分区：
文献类型：
--
作者：
W. F. Noh
Von Neumann和Richtmyer的人工粘性(Q)方法是一种非常有用的数值方法，用于跟踪流动中出现的任何地方的激波。然而，我们指出必须谨慎使用它，因为在一些强激波计算中可能会出现严重的Q引起的误差(约为100%)。我们研究了三种类型的Q误差：1.Q误差，其中有两种类型：(A)激波形成时的壁面过热和(B)无激波Q热；2.激波在非均匀网格上传播时的Q误差；3.球面几何中传播激波的Q误差。作为比较的基础，我们使用拉格朗日公式Q=C02ϱL2(UX)2作为我们的标准。该标准Q与Noh的(Q&H)激波跟踪法以及Colella和Woodward的(非Q)分段抛物线方法进行了比较。对于我们的测试问题，(Q&H)方法和PPM(特别是在使用自适应激波跟踪网格时)都给出了更好的结果。在球面几何中，流体动力学方程的Schulz和Whalen张量Q公式比标准Q公式更精确，当Schulz公式与Noh(Q&H)方法相结合时，得到了更好的结果。
The artificial viscosity (Q) method of von Neumann and Richtmyer is a tremendously useful numerical technique for following shocks wherever and whenever they appear in the flow. We show that it must be used with some caution, however, as seriousQ-induced errors (on the order of 100%) can occur in some strong shock calculations. We investigate three types ofQerrors: 1. ExcessQheating, of which there are two types: (a) excess wall heating on shock formation and (b) shocklessQheating; 2.Qerrors when shocks are propagated over a nonuniform mesh; and 3.Qerrors in propagating shocks in spherical geometry. As a basis of comparison, we use as our standard the Lagrangian formulation withQ=C02ϱl2(ux)2. This standardQis compared with Noh's (Q & H) shock-following method, which employs an artificial heat flux (H) in addition toQ, and with the (non-Q) piecewise-parabolic method (PPM) of Colella and Woodward. Both the (Q & H) method and PPM (particularly when used with an adaptive shock-tracking mesh) give superior results for our test problems. In spherical geometry, Schulz's and Whalen's tensorQformulations of the hydrodynamic equations prove to be more accurate than the standardQformulation, and when Schulz's formulation is combined with Noh's (Q & H) method, superior results are achieved.