Conservation laws for free-boundary fluid layers
Conservation laws for free-boundary fluid layers
复制标题
自由边界流体层守恒定律
DOI：
--
复制
发表时间：
2020
影响因子：
1.9
通讯作者：
E. Bueler
中科院分区：
文献类型：
--
作者：
E. Bueler
薄层中流体运动的时变模型，受有符号源项的影响，代表了气候动力学中的重要子问题。例子包括冰盖，海冰，甚至浅海和湖泊。我们解决这些问题的连续空间弱配方，即（单调）变分不等式或互补问题，其中的保守量是层厚度的离散时间序列。在这种模型中，厚度和质量通量在流体层的边缘都趋于零的自由边界通常出现。在证明这些问题在几种情况下是适定的之后，我们考虑了数值方案中离散守恒或平衡的局限性。一个自由边界的区域内的负源-烧蚀引起的利润-原来是一个障碍，以精确平衡的数值方案（无论是在连续或离散空间意义上）。我们提出了可计算的后验量，允许保守误差会计有限体积和元素计划。
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 or balance in numerical schemes. A free boundary in a region of negative source -- an ablation-caused margin -- turns out to be a barrier to exact balance for a numerical scheme (in either a continuous- or discrete-space sense). We propose computable \emph{a posteriori} quantities which allow conservation-error accounting in finite volume and element schemes.
稳定的浅冰盖作为障碍问题：适定性和有限元近似
DOI：
10.1137/110856654
发表时间：
2012
期刊：
SIAM J. Appl. Math.
影响因子：
--
作者：
G. Jouvet;E. Bueler
通讯作者：
E. Bueler