论文标题
均衡的阳性保留细胞vertex有限体积方法，可满足地表水流和标量传输耦合模型的离散最小原理
A well-balanced positivity preserving cell-vertex finite volume method satisfying the discrete maximum-minimum principle for coupled models of surface water flow and scalar transport
论文作者
论文摘要
我们使用非结构化的网格vertex网格开发了一种新的有限体积方法，用于耦合系统建模浅水流和复杂底部地形上的溶质传输。为水面高程和污染物的浓度提出了新型均衡的阳性保留离散化技术。对于流体动力学系统，提出的方案保留了静止的湖泊稳定状态和水深的积极性。对于标量传输方程，提出的方法保证了标量浓度的阳性和完美平衡。在没有被动污染物的来源项的情况下，在任何流体动力场和复杂地形的时间和时间上保留了恒定浓度状态。重要的是，这是我们方法的主要特征之一，是针对水面高程和浓度提出的新型重建技术满足溶质浓度的离散最小最小原理。我们在一系列的数值测试中证明了所提出方法的均衡和阳性特性以及我们技术的准确性及其在预测浅水传输模型的解决方案方面具有潜在的优势。
We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization techniques are proposed for the water surface elevation and the concentration of the pollutant. For the hydrodynamic system, the proposed scheme preserves the steady state of a lake at rest and the positivity of the water depth. For the scalar transport equation, the proposed method guarantees the positivity and a perfect balance of the scalar concentration. The constant-concentration states are preserved in space and time for any hydrodynamic field and complex topography in the absence of source terms of the passive pollutant. Importantly and this is one of the main features of our approach is that the novel reconstruction techniques proposed for the water surface elevation and concentration satisfy the discrete maximum-minimum principle for the solute concentration. We demonstrate, in a series of numerical tests, the well-balanced and positivity properties of the proposed method and the accuracy of our techniques and their potential advantages in predicting the solutions of the shallow water-transport model.
