Numerical methods of Lagrangian points and particles for one-dimensional wave gas-dynamics equations

In this paper, an approach is formulated to construct numerical methods of computational gas dynamics based on the approximation of the second-order nonlinear wave equations (NWE) in time and spatial variables. The NWE approach enables the construction of finite-difference and finite-element schemes with the balance (conservation) cells both in the form of finite volumes and Lagrangian points and particles. That is why the numerical methods based on the NWE approximation are of great interest for the solution of both one-dimensional (1D) and multidimensional problems of gas dynamics. In this work, we construct and study discrete NWE models for 1D problems of gas dynamics in Lagrangian variables and discuss the results of numerical experiments.