第三阶有限体积/有限元解法用于完全非线性弱散射塞雷方程
Third-order Finite Volume/Finite Element Solution of the Fully Nonlinear Weakly Dispersive Serre Equations
AI总结：
本文提出一种第三阶精度的混合方法，通过有限体积法和有限元法求解完全非线性弱散射塞雷方程，改进了高阶色散项的处理，提高了计算精度和稳定性。
摘要：
非线性弱色散塞雷方程包含高阶色散项，其中混合导数通量项难以数值处理。通过将混合空间和时间导数色散项替换为时间和空间项的组合，重新编写塞雷方程，使其系统仅包含同源导数项。改写后的塞雷方程包含水深和一个新量作为守恒变量，使用有限体积法进行演算。剩余的原始变量，即速度，通过求解一个二阶椭圆方程得到。为避免引入可能主导物理色散的数值色散，该混合方案具有第三阶精度。通过解析解、实验室水槽数据和坝溃坝问题模拟，证明了该方案在多种问题中准确、易于实现且稳定，包括不连续流。
英文摘要：
The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. The mix spatial and temporal derivative dispersive term is replaced by a combination of temporal and spatial terms. The Serre equations are re-written so that the system of equations contain homogeneous derivative terms only. The reformulated Serre equations involve the water depth and a new quantity as the conserved variables which are evolved using the finite volume method. The remaining primitive variable, the velocity is obtained by solving a second-order elliptic equation using the finite element method. To avoid the introduction of numerical dispersion that may dominate the physical dispersion, the hybrid scheme has third-order accuracy. Using analytical solutions, laboratory flume data and by simulating the dam-break problem, the proposed scheme is shown to be accurate, simple to implement and stable for a range of problems, including discontinuous flows.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
