带约束的正压和不可压流体模式的多辛变分积分
Multisymplectic variational integrators for barotropic and incompressible fluid models with constraints
摘要：
我们提出了一个结构保持离散化的基本时空几何结构的流体力学的拉格朗日描述在2D和3D。在此基础上，发展了正压不可压流体模型的多辛变分积分器，满足离散形式的Noether定理。我们展示了如何几何积分器可以处理经常在真空中的流体运动与自由边界和约束，如对一个障碍物的流体在表面上流动的影响。我们的方法是适用于广泛的模型，包括Boussinesq和浅水模型，适当选择的拉格朗日。
英文摘要：
We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for barotropic and incompressible fluid models, which satisfy a discrete version of Noether theorem. We show how the geometric integrator can handle regular fluid motion in vacuum with free boundaries and constraints such as the impact against an obstacle of a fluid flowing on a surface. Our approach is applicable to a wide range of models including the Boussinesq and shallow water models, by appropriate choice of the Lagrangian.
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