An iterative method for solving difference problems of gas dynamics in the mixed Euler-Lagrangian variables

Abstract The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on simplex system of equations gas dynamics in the mixed Euler-Lagrangian variables. To find solution such scheme at time step, it represented as single equation nonlinear function two arguments from space – direct product spaces gas-dynamic quantities. an equation, combination generalized Gauss-Seidel iterative (external iterations) and two-layer iteration (internal iterations each external iteration) used. feature that, which solved by internal iterations, obtained using symmetrization non-degenerate linear transformation that this has self-adjoint positive Frechet derivative.