A new front tracking method using particles with extended location information

Abstract A new front tracking method is developed through using Lagrangian particles marked by their extended location information (ELI) including the location coordinates and the spatial derivatives of the location coordinates. The new method is capable of providing more accurate descriptions for the geometrical features of the interface than the conventional front tracking (CFT) methods due to three key originalities. First, high order numerical schemes that can be used to evaluate the ELI of the interpolated particles with high order accuracy are developed based on the ELI of two given particles. Second, a series of evolution equations are derived on the need of tracking the ELI of all the particles during the interface evolving. Third, transformation formulae are derived for the use of modifying the spatial derivatives of the particles' location coordinates such that large amplitudes of which can be avoided. Performances of the new method are demonstrated through standard benchmark tests.