论文标题
在Quadtree网格上的自适应中央风方案，用于可变密度浅水方程
An adaptive central-upwind scheme on quadtree grids for variable density shallow water equations
论文作者
论文摘要
最小化计算成本是流体动力学建模和数值分析的主要挑战之一，而实现这一目标的方法之一是使用Quadtree网格。在本文中，我们在Quadtree网格上提出了一个自适应方案，以易变密度浅水方程。耦合系统的方案是根据[18]中提出的具有均衡阳性的中央风向方案而开发的。该方案能够准确保留“湖泊湖泊”的稳态。底部地形函数的连续分段双线性插值用于在空间中实现高阶，以保留每个计算单元的点值的水深阳性。检查必要的条件以保持水深度和密度的积极性，并确保实现稳定的数值方案。在每个时间步长，检查局部梯度，以找到新的种子点，以局部完善/更加计算网格。
Minimizing computational cost is one of the major challenges in the modelling and numerical analysis of hydrodynamics, and one of the ways to achieve this is by the use of quadtree grids. In this paper, we present an adaptive scheme on quadtree grids for variable density shallow water equations. A scheme for the coupled system is developed based on the well-balanced positivity-preserving central-upwind scheme proposed in [18]. The scheme is capable of exactly preserving "lake-at-rest" steady states. A continuous piecewise bi-linear interpolation of the bottom topography function is used to achieve higher-order in space in order to preserve the positivity of water depth for the point values of each computational cell. Necessary conditions are checked to be able to preserve the positivity of water depth and density, and to ensure the achievement of a stable numerical scheme. At each timestep, local gradients are examined to find new seeding points to locally refine/coarsen the computational grid.
