An implicit Lagrangian–Eulerian ЕМВ-method for solving two-dimensional hydrodynamic equations on unstructured meshes

The paper presents an ALE method for solving hydrodynamic equations on unstructured meshes. It is based on an implicit finite-volume scheme derived with Godunov's approach. The basic quantities — destiny, temperature and velocity are stored in cell centers. For relations between pressure and velocities in the centers and their analogs in the nodes, we use those proposed by P.-H. Maire et al. A piecewise linear TVD reconstruction of pressure and velocity in the cell is used achieve the second order of approximation keeping monotonicity of smooth solutions.
Mesh rezoning during the calculation is implemented. The quantities are recalculated through mapping the old mesh onto the new one. A limited piecewise linear representation is used for quantities in the cells of the old mesh and interface in the mixed cells are reconstructed with the VOF method. Mass, momentum and total energy are conserved.