论文标题
完全耦合时间依赖的stokes/darcy-transport问题的可杂交不连续的盖尔金方法
A hybridizable discontinuous Galerkin method for the fully coupled time-dependent Stokes/Darcy-transport problem
论文作者
论文摘要
我们提出了一种用于完全耦合的时间依赖性的stokes-darcy-transport问题的高阶杂交不连续的Galerkin（HDG）方法，其中流体粘度和源/接收器项取决于浓度和分散/扩散张量取决于流体速度。这种HDG方法使离散流程方程与离散传输方程兼容。此外，HDG方法可以保证$ H^{\ rm div} $ Sense中的强大质量保护，并且自然地通过FaceT变量来处理Stokes和Darcy区域之间的界面条件。我们采用线性化的去耦策略，其中Stokes/Darcy和传输方程是通过延时浓度顺序求解的。我们证明了适当的和最佳的速度和能量规范浓度的先验误差估计。我们提出了尊重流量和运输离散化的兼容性的数值示例，并证明离散解决方案相对于问题参数是可靠的。
We present a high-order hybridized discontinuous Galerkin (HDG) method for the fully coupled time-dependent Stokes-Darcy-transport problem where the fluid viscosity and source/sink terms depend on the concentration and the dispersion/diffusion tensor depends on the fluid velocity. This HDG method is such that the discrete flow equations are compatible with the discrete transport equation. Furthermore, the HDG method guarantees strong mass conservation in the $H^{\rm div}$ sense and naturally treats the interface conditions between the Stokes and Darcy regions via facet variables. We employ a linearizing decoupling strategy where the Stokes/Darcy and the transport equations are solved sequentially by time-lagging the concentration. We prove well-posedness and optimal a priori error estimates for the velocity and the concentration in the energy norm. We present numerical examples that respect compatibility of the flow and transport discretizations and demonstrate that the discrete solution is robust with respect to the problem parameters.
