基于分区径向基函数的Level Set界面捕捉研究

Regional RBF based Level Set Method for Interface Capturing

针对传统的Level Set方法的固有缺陷,通过引入径向基函数(radial basis function,RBF),提出一种分区捕捉动界面的Level Set数值方法,将Level Set偏微分控制方程转化为全微分方程,避免了重新初始化过程,可精确表达界面形状并维持质量守恒.采用径向基函数中的基函数和权重系数来重构符号距离函数,并结合区域划分技术提高计算效率.3个计算算例表明,基于分区径向基函数Level-Set方法,可明显提高界面几何形状的精度和捕捉效率,具有较好的质量守恒性.

The renewal of signed distance function usually relies on reinitialization in conventional Level Set method. An alternative method is proposed in this paper to regionally capture the moving inter- faces via the introduction of the Radial Basis Functions （RBF）. This approach provides an accuracy and conserved representation of the implicit function, location and shape of interfaces. The signed dis- lance function is rebuilt by based functions and weight coefficients. Its deformation is then considered as an updating of the RBF interpolants, turning the partial differential equation （PDE） problem into an ordinary differential equation （ODE） problem. Reinitialization is found to be no longer necessary and hence it avoids large numerical errors occurring in the conventional method. Three numerical ex amples show that the proposed regional RBF Based Level Set method can significantly improve both the accuracy and conservation in capturing moving interfaces.