66 citations · 304 across the 25 of their papers we have counts for
4 papers · 1 filter
One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes
Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko
The paper considers one-dimensional flows of a polytropic gas in the Lagrangian coordinates in three cases: plain one-dimensional flows, radially symmetric flows and spherically sy…
Invariant conservative difference schemes for shallow water equations in Eulerian and Lagrangian coordinates
V. A. Dorodnitsyn, E. I. Kaptsov
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and…
Symmetries, conservation laws, invariant solutions and difference schemes of the one-dimensional Green-Naghdi equations
V. A. Dorodnitsyn, E. I. Kaptsov, S. V. Meleshko
The paper is devoted to the Lie group properties of the one-dimensional Green-Naghdi equations describing the behavior of fluid flow over uneven bottom topography. The bottom topog…
Invariant Conservation Law-Preserving Discretizations of Linear and Nonlinear Wave Equations
A. F. Cheviakov, V. A. Dorodnitsyn, E. I. Kaptsov
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, u…