Plane one-dimensional MHD flows: Symmetries and conservation laws

@article{Dorodnitsyn2021PlaneOM,
  title={Plane one-dimensional MHD flows: Symmetries and conservation laws},
  author={V. A. Dorodnitsyn and E. I. Kaptsov and Roman Kozlov and Sergey V. Meleshko and Potcharapol Mukdasanit},
  journal={International Journal of Non-Linear Mechanics},
  year={2021}
}
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and conservation laws. For the case of the finite electric conductivity we establish Lie group classification, i.e. we describe all cases of the conductivity σ(ρ, p) for which there are symmetry extensions. The conservation laws are derived by the direct computation… 
1 Citations

Tables from this paper

Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations
TLDR
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity and new schemes are constructed for the case of finite conductivity.

References

SHOWING 1-10 OF 32 REFERENCES
One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: Symmetry classification, conservation laws, difference schemes
TLDR
A comprehensive analysis of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates is performed, given by a single second-order partial differential equation, which results in conservation laws being obtained.
Natural curvilinear coordinates for ideal MHD equations. Non-stationary flows with constant total pressure
Abstract Equations of magnetohydrodynamics (MHD) in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the non-linear
Exact solutions to the ideal magneto-gas-dynamics equations through Lie group analysis and substitution principles
In this paper, we consider the equations governing an inviscid, thermally non-conducting fluid of infinite electrical conductivity in the presence of a magnetic field and subject to no extraneous
Exact Solutions of Stationary Equations of Ideal Magnetohydrodynamics in the Natural Coordinate System
Equations of ideal magnetohydrodynamics that describe stationary flows of an inviscid ideally electrically conducting fluid are considered. Classes of exact solutions of these equations are
Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics
Abstract The conservation laws for second order scalar partial differential equations and systems of partial differential equations which occur in fluid mechanics are constructed using different
Group properties and solutions for the 1D Hall MHD system in the cold plasma approximation
We study the Lie point symmetries and the similarity transformations for the partial differential equations of the nonlinear one-dimensional magnetohydrodynamic system with the Hall term known as
Some exact solutions of the ideal MHD equations through symmetry reduction method
Abstract We use the symmetry reduction method based on Lie group theory to obtain some exact solutions, the so-called invariant solutions, of the ideal magnetohydrodynamic equations in ( 3 + 1 )
Group analysis of the Fourier transform of the spatially homogeneous and isotropic Boltzmann equation with a source term
Abstract The paper is devoted to group analysis of the spatially homogeneous and isotropic Boltzmann equation with a source term. In fact, the Fourier transform of the Boltzmann equation with respect
Fluid Mechanics
Ludwig Krinner (Dated: November 5th 2012) Abstract This is a script made with the help of Landau Lifshitz, Book VI [1] on fluid mechanics, that gives a short introduction to basic fluid mechanics.
Nonlinear self-adjointness and conservation laws
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict
...
1
2
3
4
...