A new method is developed to approximate a first-order Hamilton–Jacobi equation. The constant motion of an interface in the normal direction is of interest. The interface is captured with the help of a “Level-Set” function approximated through a finite-volume Godunov-type scheme. Contrarily to most computational approaches that consider smooth Level-Set functions, the present one considers sharp “Level-Set”, the numerical diffusion being controlled with the help of the Overbee limiter (Chiapolino et al. in J Comput Phys 340:389–417, 2017). The method requires gradient computation that is addressed through the least squares approximation. Multidimensional results on fixed unstructured meshes are provided and checked against analytical solutions. Geometrical properties such as interfacial area and volume computation are addressed as well. Results show excellent agreement with the exact solutions.

开发了一种新方法来近似一阶汉密尔顿-雅各比方程。界面在法线方向上的恒定运动是令人关注的。该接口是借助“ Level-Set”功能捕获的，该功能通过有限体积的Godunov型方案近似。与大多数考虑平滑Level-Set函数的计算方法相反，本方法考虑了尖锐的“ Level-Set”，借助于Overbee限制器来控制数值扩散（Chiapolino等人，J Comput Phys 340：389-417）。 ，2017）。该方法需要通过最小二乘近似来解决的梯度计算。提供了固定的非结构化网格上的多维结果，并根据分析解决方案进行了检查。还解决了几何属性，例如界面面积和体积计算。