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Behavior of viscous solutions in Lagrangian formulation

机译：拉格朗日公式中粘性溶液的行为

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In this paper, the behavior of shock-capturing methods in Lagrangian coordinate is investigated. The relation between viscous shock and inviscid one is analyzed quantitatively, and the procedure of a viscous shock formation and propagation with a jump type initial data is described. In general, a viscous shock profile and a discontinuous one include different energy and momentum, and these discrepancies result in the generation of waves in all families when a single wave Riemann problem (shock or rarefaction) is solved. Employing this method, some anomalous behavior, such as, viscous shock interaction, shock passing through ununiform grids, postshock oscillations and lower density phenomenon is explained well. Using some classical schemes to solve the inviscid flow in Lagrangian coordinate may be not adequate enough to correctly describe flow motion in the discretized space. Partial discrepancies between von Neumann artificial viscosity method and Godunov method are exhibited. Some reviews are given to those methods which can ameliorate even eliminate entropy errors. A hybrid scheme based on the understanding to the behavior of viscous solution is proposed to suppress the overheating error.
机译：本文研究了拉格朗日坐标系中的捕捉方法的行为。定量分析了粘性激波与无粘性激波之间的关系，并描述了具有跳跃型初始数据的粘性激波的形成和传播过程。通常，粘性的冲击轮廓和不连续的冲击轮廓包含不同的能量和动量，而这些差异会导致在解决单波黎曼问题（冲击或稀疏）时在所有族中产生波。使用这种方法，可以很好地解释一些异常行为，例如粘性冲击相互作用，穿过不均匀网格的冲击，震后振荡和低密度现象。使用一些经典方案来求解拉格朗日坐标中的无粘性流可能不足以正确地描述离散空间中的流运动。冯·诺依曼人工粘度法与Godunov方法之间存在部分差异。对可以改善甚至消除熵误差的那些方法进行了一些评论。提出了一种基于对粘性溶液行为的理解的混合方案来抑制过热误差。

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