论文标题
自由液体层的保护法
Conservation laws for free-boundary fluid layers
论文作者
论文摘要
薄层中流体运动的时间依赖性模型，受到签名的源项，代表了气候动力学中的重要子问题。例子包括冰盖，海冰，甚至是浅海和湖泊。我们将这些问题作为连续空间弱制剂的离散时间序列，即（单调）变化不平等或互补性问题，其中保守数量是层厚度。在此类模型中，厚度和质量通量在流体层边缘的厚度和质量通量都在零上零。在显示这些问题的情况下，在几种情况下，我们考虑了数值方案中离散保护的局限性。负源区域中的自由边界 - 消融缘的边缘 - 事实证明是在连续或离散空间的感觉中确切保护的障碍。然后，我们提出了可计算的后验数量，该量允许有限体积和有限元方案中的保护界限。
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these problems as discrete-time sequences of continuous-space weak formulations, namely (monotone) variational inequalities or complementarity problems, in which the conserved quantity is the layer thickness. Free boundaries wherein the thickness and mass flux both go to zero at the margin of the fluid layer generically arise in such models. After showing these problems are well-posed in several cases, we consider the limitations to discrete conservation in numerical schemes. A free boundary in a region of negative source -- an ablation-caused margin -- turns out to be a barrier to exact conservation in either a continuous- or discrete-space sense. We then propose computable a posteriori quantities which allow conservation-error bounds in finite volume and finite element schemes.
