轴对称坐标系下含曲率的水平集方程在非结构网格上的数值方法

为了在三角形和四边形网格上采用水平集方法模拟轴对称爆轰波阵面与曲率相关的运动,假设爆 轰波阵面的法向速度是曲率的线性函数,通过坐标变换得到了轴对称坐标系下的水平集方程。水平集方程的 曲率无关项采用正格式离散,曲率项采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式。算例表 明,在轴对称三角形网格和四边形网格上,含曲率的水平集方程的离散格式为强一阶精度。给出了三角形和 四边形混合网格上不光滑界面以曲率收缩的运动过程,收缩过程未出现不稳定现象。多个爆轰波阵面相互作 用的算例说明本文的格式可有效地模拟曲率相关的爆轰波的相互作用问题

Numerical scheme for level set equations containing curvature on axisymmetric unstructured meshes

To simulate the moving of axisymmetric detonation front on triangles and quadrilaterals using the level set method,assuming that the detonation normal velocity is the linear function of curvature,an axisymmtric level set equation is gained by the use of coordinate transformation.The convection term of the level set equation is solved by the positive scheme,and the curvature term is solved by the Galerkin isoparametric finite element method and the semi-implicit time stepping technique.On triangles and quadrilaterals,the scheme of the level set equations containing curvature is higher than first order accuracy in L2 and L∞ norms.The computational example is given of nonsmooth level sets shortening stably by the local curvature on the unstructured mixed meshes.The example of multiple detonation fronts colliding shows that the scheme of this paper can be used to simulate the propagation of detonation front on curvature.