We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulation is presented and proven hyperbolic. It induces a corresponding finite-volume scheme that is specifically taylored for uncertain velocities.

翻译：我们提出了一种新方法，用于确定速度场不确定性下水平集的演化。该方法导出了水平集的随机描述。为计算随机水平集的分位数，我们对水平集方程的双曲重构形式应用了随机伽辽金法。我们提出了一种新型内嵌式伽辽金公式，并证明了其双曲性，由此推导出专为不确定速度设计的相应有限体积格式。