论文标题
带有自适应网格精炼的笛卡尔网格活动通量法
The Cartesian Grid Active Flux Method with Adaptive Mesh Refinement
论文作者
论文摘要
我们介绍了在自适应精致的笛卡尔网格上的首次实现。主动通量方法是用于双曲线保护定律的三阶准确体积方法，该方法基于点值以及保守量的细胞平均值。最终的方法具有紧凑的模具，并具有良好的稳定性。 该方法是在Forestclaw中实现的，该求解器是一种用于平行自适应网状基于贴片的求解器的软件。在每个笛卡尔网格贴片上，都可以应用单个网格活动通量方法。网格贴片之间的数据交换是通过幽灵细胞组织的。空间和时间上的本地模具以及用于重建的点值的可用性，可导致有效的实现。最终的方法是三阶准确，保守的，并允许及时使用亚度性。
We present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point values as well as cell average values of the conserved quantities. The resulting method has a compact stencil in space and time and good stability properties. The method is implemented as a new solver in ForestClaw, a software for parallel adaptive mesh refinement of patch-based solvers. On each Cartesian grid patch the single grid Active Flux method can be applied. The exchange of data between grid patches is organised via ghost cells. The local stencil in space and time and the availability of the point values that are used for the reconstruction, leads to an efficient implementation. The resulting method is third order accurate, conservative and allows the use of subcycling in time.
