Influence of The Smoothing Parameter in The Re-initialization Equation on The Level Set Interface-capturing

The level set method is frequently used to simulate and capture the moving interface in the molten metal casting and forming field. However, the level set function has to be re-initialized after several time-steps. And influence of the smoothing parameter on numerical accuracy of the moving interface-capturing is mainly investigated in the present work, which existing in the implicit iteration re-initialization equation. Further, a novel smoothing parameter approximation is derived and proposed, which keeping almost the interface location motionless while re-initialization. Several typical cases are compared to simulate with the other smoothing parameter approximations proposed in some relative literatures. To diminish numerical scheme's effect, some high order numerical methods in space and time are employed in the simulation. Results evidently show that the smoothing parameter has a strong impact on simulation accuracy of the moving interface-capturing. Meanwhile, compare with the other approximations, it is found that all results computed with the novel smoothing parameter approximation are best. It can greatly improve capturing accuracy of the moving interface. That's to say, it can dramatically decrease the mass loss and capture the sharp interface with high resolution, especially for moving interface with the complicated topological geometry change.