The numerical method of Lagrange particles on the basis of two dimentional gas dynamics wave equations

In the paper we formulate the numerical method of particles based on the approximation of the system of gas dynamics equations in the form of second order nonlinear wave equations (NWE) in time and space variables. On the basis of "NWE" it allows one to construct finite difference and finite elements schemes with cells of balance both in the "finite volume" and lagrange "particles" framework. The investigation of the method of particles and numerical tests are performed for two dimensional gas dynamics problems in the Lagrange form on triangular grids.