| 摘要: |
| 在某些特定条件下,Richards方程的解在时空上呈现陡峭的锋面。为能有效地模拟具有对流占优特性的非饱和多孔介质中的水流问题,推广一种内部惩罚间断有限元(Interior penalty discontinuous Galerkin,IPDG)方法应用于一维非饱和土壤水入渗问题的模拟。针对具有van Genuchten-Mualem模型和Dirichlet入渗边界条件的Richards方程,分别采用间断有限元法和标准有限元方法求解。借助于相对L2模和相对最大模误差进行讨论。几种不同质地的均质土壤水入渗的数值算例结果表明:相比标准有限元方法,间断有限元方法在选取的4种不同网格剖分单元结点上能够有效地模拟非饱和对流占优土壤水流问题,并且能够获得准确的全局质量守恒。 |
| 关键词: 土壤水流 对流占优 Richards方程 间断有限元 |
| DOI：10.11841/j.issn.1007-4333.2015.01.021 |
| 投稿时间：2014-04-04 |
| 基金项目:国家自然科学基金重点项目(51039007) |
|
| Application of the discontinuous Galerkin method to simulate convection-dominated soil water flow problems in one-dimension |
|
HUANG Wen-zhu
|
| (College of Resources and Environmental Sciences, China Agricultural University, Beijing 100193, China) |
| Abstract: |
| Richards equation is the most common model used to describe water flow in the vadose zone,which can yield solutions with sharp fronts in space and time under certain conditions.To effectively simulate unsaturated flow in porous media for convection-dominated problem,discontinuous Galerkin (DG) methods with penalty was proposed.The method was applied to simulate one-dimension unsaturated infiltration problem.Interior penalty discontinuous Galerkin (IPDG) method and standard finite elements method (FEM) were both used to solve the Richards equation with van Genuchten-Mualem model and Dirichlet conditions.Different soil numerical simulated results showed that DG method could effectively simulate the unsaturated water flow in the specific soils for convection-dominated problem on several nets.DG method solution could excellently approximate to the exact solution.The numerical experiments also demonstrated that DG method could achieve accurate global mass balance. |
| Key words: soil water flow convection-dominated Richards equation discontinuous Galerkin method |
