一种用于非线性自由表面流的界面追踪时空可混合/嵌入式间断伽辽金方法
An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows
中文总结 AI 辅助
本文提出一种时空可混合/嵌入式间断伽辽金方法，用于非线性自由表面流，通过水平集函数追踪双流体尖锐界面，实现无需平滑或额外稳定项的界面追踪。
中文摘要 AI 辅助
我们提出了一种兼容的时空可混合/嵌入式间断伽辽金离散方法，用于非线性自由表面波。我们在双流体（液体和气体）域中提出该问题，并使用时间相关的水平集函数来识别两种流体之间的尖锐界面。不可压缩双流体方程通过精确质量守恒的时空可混合间断伽辽金方法进行离散，而水平集方程则通过时空嵌入式间断伽辽金方法进行离散。与其他间断伽辽金方法不同的是，嵌入式间断伽辽金方法能够得到界面的连续近似。这与时空框架相结合，形成了一种无需借助平滑技术或额外网格稳定项的界面追踪方法。
英文摘要
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to identify the sharp interface between the two fluids. The incompressible two-fluidd equations are discretized by an exactly mass conserving space-time hybridizable discontinuous Galerkin method while the level-set equation is discretized by a space-time embedded discontinuous Galerkin method. Different from alternative discontinuous Galerkin methods is that the embedded discontinuous Galerkin method results in a continuous approximation of the interface. This, in combination with the space-time framework, results in an interface-tracking method without resorting to smoothing techniques or additional mesh stabilization terms.
