论文标题
在无限域中，无缝的，扩展的DG方法，用于对流扩散问题
A seamless, extended DG approach for advection-diffusion problems on unbounded domains
论文作者
论文摘要
我们提出和分析了半无限域域上对流扩散方程的无缝扩展不连续的Galerkin（DG）离散化。半无限的半线分为有限的子域，该子域使用标准的多项式基础，并使用半障碍子域，将缩放的laguerre函数用作基础和测试函数。数值通量可以以与标准单域DG Interlement通量相同的方式在两个子域之间的界面处的耦合。关于扩展DG模型的新型线性分析相对于Péclet数量产生无条件的稳定性。由于使用线性对流扩散和粘性汉堡方程的数值实验中突出显示，由于在域的不同部分上使用了不同的基集函数引起的错误。由于在半无限子域上增加了阻尼项，扩展框架能够有效地模拟吸收边界条件，而无需在接口处其他条件。与给定的计算成本相比，在半无限子域中的几种模式足以比标准方法更准确地处理单个波和波训练信号，从而为无界区域的流体流量模拟提供了吸引人的模型。
We propose and analyze a seamless extended Discontinuous Galerkin (DG) discretization of advection-diffusion equations on semi-infinite domains. The semi-infinite half line is split into a finite subdomain where the model uses a standard polynomial basis, and a semi-unbounded subdomain where scaled Laguerre functions are employed as basis and test functions. Numerical fluxes enable the coupling at the interface between the two subdomains in the same way as standard single domain DG interelement fluxes. A novel linear analysis on the extended DG model yields unconditional stability with respect to the Péclet number. Errors due to the use of different sets of basis functions on different portions of the domain are negligible, as highlighted in numerical experiments with the linear advection-diffusion and viscous Burgers' equations. With an added damping term on the semi-infinite subdomain, the extended framework is able to efficiently simulate absorbing boundary conditions without additional conditions at the interface. A few modes in the semi-infinite subdomain are found to suffice to deal with outgoing single wave and wave train signals more accurately than standard approaches at a given computational cost, thus providing an appealing model for fluid flow simulations in unbounded regions.
