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Three-dimensional Eulerian method for large deformation of viscoelastic fluid: Toward plate-mantle simulation

机译：粘弹性流体大变形的三维欧拉方法：向板幔模拟

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Toward the unified simulation of the large deformation of a rigid viscoelastic material (plate) and the convection of a viscous fluid (mantle), an Eulerian scheme with a semi-Lagrangian method is developed. The scheme adopts the CIP-CSLR method for advection terms of staggered grid system in three dimensions. The positive transported profile of a positive quantity is assured by flux corrections in the dimensional splitting method. The Jaumann co-rotational effect of the stress tensor is also integrated into the semi-Lagrangian treatment. This co-rotated semi-Lagrangian method is combined with an exponential time differencing method in the time development of the Maxwell constitutive model. The large time step comparable to, or larger than, the Maxwell relaxation time is successfully realized. Validation tests are performed for the three-dimensional Rayleigh-Taylor instability of a viscoelastic material with jump discontinuity of the mass density and other material properties. (C) 2008 Elsevier Inc. All rights reserved.
机译：为了对刚性粘弹性材料（板）的大变形和粘性流体（地幔）的对流进行统一模拟，开发了一种采用半拉格朗日方法的欧拉方案。该方案采用CIP-CSLR方法对三维交错网格系统的对流项进行了求解。通过分流方法中的磁通校正可以确保正量的正向传输轮廓。应力张量的Jaumann同向旋转效应也被整合到半Lagrangian处理中。在麦克斯韦本构模型的时间开发中，该同旋转半拉格朗日方法与指数时差方法相结合。成功地实现了与Maxwell弛豫时间相当或更长的较大时间步长。对粘弹性材料的三维Rayleigh-Taylor不稳定性，质量密度和其他材料特性的跳跃不连续性进行了验证测试。 （C）2008 Elsevier Inc.保留所有权利。

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