论文标题
麦克斯韦流体的粘弹性流和保护法
Viscoelastic flows of Maxwell fluids with conservation laws
论文作者
论文摘要
我们考虑了1D粘弹性流的Maxwell开创性Rheo-Logical方程的多维扩展。我们针对可压缩流的因果模型，该模型由半组解决方案定义给定初始条件，使扰动以有限的速度传播。我们提出了一种对称的保护额度系统，该系统包含较高的麦克斯韦（UCM）方程作为因果模型。该系统是多凸弹性动力学的扩展，其额外的材料度量变量可放松以建模粘性效应。有趣的是，该框架还可以涵盖其他流变方程，具体取决于材料度量变量所选的松弛极限。我们建议在因果关系很重要时将新系统应用于浅水状态下不可压缩的自由表面重力流。该系统还原为对称的浅脂肪的粘弹性2D浅水系统的粘弹性扩展，并涵盖了我们先前与F. bouchut提出的圣人的粘弹性扩展。
We consider multi-dimensional extensions of Maxwell's seminal rheo-logical equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions , and such that perturbations propagates at finite speed. We propose a symmetric hyperbolic system of conservation laws that contains the Upper-Convected Maxwell (UCM) equation as causal model. The system is an extension of polyconvex elastodynamics, with an additional material metric variable that relaxes to model viscous effects. Interestingly, the framework could also cover other rheological equations, depending on the chosen relaxation limit for the material metric variable. We propose to apply the new system to incompressible free-surface gravity flows in the shallow-water regime, when causality is important. The system reduces to a viscoelastic extension of Saint-Venant 2D shallow-water system that is symmetric-hyperbolic and that encompasses our previous viscoelastic extensions of Saint-Venant proposed with F. Bouchut.
