An adaptive mesh method for 1D hyperbolic conservation laws
An adaptive mesh method for 1D hyperbolic conservation laws
复制标题
一维双曲守恒定律的自适应网格方法
DOI：
10.1016/j.apnum.2014.10.008
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发表时间：
2015
影响因子：
2.8
通讯作者：
Hui Feng
中科院分区：
文献类型：
--
作者：
Fuxing Hu;Rong Wang;Xueyong Chen;Hui Feng
将重分区方法与有限体积加权本质无振荡（韦诺）格式相结合，提出了一种求解一维双曲守恒律方程组的自适应方法。一个后验误差估计，用于均匀分布的网格，从五阶韦诺（WENO 5）和三阶ENO（ENO 3）格式的各自的数值解之间的差异。网格数可以根据解的结构自适应地调整。为了提高效率，网格重新调整是每隔几个时间步而不是每一个时间步执行。此外，在有限体积ENO重建的基础上，采用高阶守恒插值方法，从旧网格计算新网格上的物理解。大量的例子表明，这种自适应方法具有更准确的分辨率的不连续性相似的计算时间水平相比，在一个均匀的网格。
An adaptive method is developed for solving one-dimensional systems of hyperbolic conservation laws, which combines the rezoning approach with the finite volume weighted essentially non-oscillatory (WENO) scheme. An a posteriori error estimate, used to equidistribute the mesh, is obtained from the differences between respective numerical solutions of 5th-order WENO (WENO5) and 3rd-order ENO (ENO3) schemes. The number of grids can be adaptively readjusted based on the solution structure. For higher efficiency, mesh readjustment is performed every few time steps rather than every time step. In addition, a high order conservative interpolation is used to compute the physical solutions on the new mesh from old mesh based on the finite volume ENO reconstruction. Extensive examples suggest that this adaptive method exhibits more accurate resolution of discontinuities for a similar level of computational time comparing with that on a uniform mesh.