Implicit Lagrangian-Eulerian Tvd Method For Solving Two-Dimensional Hydrodynamic Equations On Unstructured Meshes

An ALE method for solving hydrodynamic equations on unstructured meshes is presented. It is based on an implicit finite-volume scheme derived in Godunov’s approach. The basic quantities (the density, temperature, and velocity) are defined at cell centers. For relations between pressure and velocities at the centers and their analogs at the nodes, we use the relations proposed by P.H. Maire et al. A piecewise-linear TVD reconstruction of the pressure and velocity in the cell is used to achieve the second-order approximation of smooth solutions, preserving their monotonicity. Mesh rezonings are implemented during the calculation. To recalculate the values, the old mesh is covered onto the new one so that a bounded piecewise-linear representation is used for the values in the cells of the old mesh, while the interface in the mixed cells is reconstructed by the VOF method. The mass, momentum, and total energy are conserved under the recalculation. © 2018, Pleiades Publishing, Ltd.