A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes
A Stabilized Finite Volume Element Formulation for Sedimentation-Consolidation Processes
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DOI：
10.1137/110836559
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发表时间：
2012-05
期刊：
影响因子：
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通讯作者：
R. Bürger;R. Ruiz-Baier;Héctor Torres
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文献类型：
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作者：
R. Bürger;R. Ruiz-Baier;Héctor Torres
所谓澄清器-浓缩器单元中的沉降-固结过程模型由描述局部固体浓度演变的抛物线方程以及描述混合物运动的不可压缩流体的斯托克斯系统的版本给出。在柱坐标系中，如果假设轴对称解，则原始问题会简化为二维空间。这就带来了困难，即用于构建数值格式的子空间涉及加权索博列夫空间。引入了一种新颖的有限体积元方法进行空间离散，其中速度场和固体浓度在两个不同的双网格上离散。该方法基于浓度场的稳定不连续伽辽金公式，以及分别用于速度和压力的一对多尺度稳定的 $\mathbb{P}_1$-$\mathbb{P}_1$ 元素。数值实验说明了模型的特性和令人满意的结果...
A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid describing the motion of the mixture. In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem reduces to two space dimensions. This poses the difficulty that the subspaces for the construction of a numerical scheme involve weighted Sobolev spaces. A novel finite volume element method is introduced for the spatial discretization, where the velocity field and the solids concentration are discretized on two different dual meshes. The method is based on a stabilized discontinuous Galerkin formulation for the concentration field, and a multiscale stabilized pair of $\mathbb{P}_1$-$\mathbb{P}_1$ elements for velocity and pressure, respectively. Numerical experiments illustrate properties of the model and the satisfactory p...