A partition-coupled Eulerian-Lagrangian method for large-deformation simulation of compressible fluid

We present a partition-coupled Eulerian-Lagrangian method (PCELM) for accurately tracking a free interface and a contact discontinuity of the compressible fluid with large deformation. This method tracks the interface by arranging splittable Lagrangian particles on an Eulerian grid and adopts a partition-weighted bidirectional mapping between particles and grids using a cubic B-spline as interpolation function. PCELM suppresses oscillation of the discontinuous surface by this partition-weighted remapping method and solves the problem of numerical fracture by a particle splitting method. A virtual particle method is also proposed to deal with discontinuity of particle flow at the boundary and to maintain interpolation accuracy at the boundary. The conservation of mass, momentum, and energy of PCELM is proved by conservation analysis. Accuracy tests and simulations of discontinuous surfaces and free interfaces are performed to verify the accuracy and stability of PCELM. The results show that PCELM has strong energy conservation and low energy dissipation and that it is not only better at suppressing oscillations than the original method, but can also simulate a compressible fluid with large deformation more accurately than weighted essentially nonoscillatory schemes.