论文标题
Tikhonov的方法，用于设置曲率计算
A Tikhonov approach to level set curvature computation
论文作者
论文摘要
在两相流的数值模拟中，界面曲率的计算是至关重要的成分。使用有限元和级别设置离散化，离散接口通常是低阶多项式的级别集，这通常会导致接口曲率的近似值较差。我们使用Sobolev Space $ H^2 $或$ H^3 $的$ L^2 $投影运算符的大致反转提出了一种曲率计算的方法。对于近似近方的有限元计算，所得的高阶方程被重新重新构成二阶方程系统。由于Tikhonov的正则化，该方法被证明在离散违规行为上是稳定的。显示了用于内部界面以及与域边界相交的界面的数值示例。
In numerical simulations of two-phase flows, the computation of the curvature of the interface is a crucial ingredient. Using a finite element and level set discretization, the discrete interface is typically the level set of a low order polynomial, which often results in a poor approximation of the interface curvature. We present an approach to curvature computation using an approximate inversion of the $L^2$ projection operator from the Sobolev space $H^2$ or $H^3$. For finite element computation of the approximate inverse, the resulting higher order equation is reformulated as a system of second order equations. Due to the Tikhonov regularization, the method is demonstrated to be stable against discretization irregularities. Numerical examples are shown for interior interfaces as well as interfaces intersecting the boundary of the domain.
