Parker’s Solar Wind Model for a Polytropic Gas

Parker’s hydrodynamic isothermal solar wind model is extended to apply for a more realistic polytropic gas flow that can be caused by a variable extended heating of the corona. A compatible theoretical formulation is given and detailed numerical and systematic asymptotic theoretical considerations are presented. The polytropic conditions favor an enhanced conversion of thermal energy in the solar wind into kinetic energy of the outward flow and are hence shown to enhance the acceleration of the solar wind, thus indicating a quicker loss of the solar angular momentum.

Reconstruction of the New Agegraphic Polytropic Gas Dark Energy Model in the Flat Friedmann Robertson Walker (FRW) Universe

In this paper, we study the Polytropic Gas Dark Energy model and New Agegraphic Dark Energy model in the flat Friedmann Robertson Walker (FRW) Universe and establish a correspondence between them for the scalar fields. This correspondence allows reconstructing the potential of the Polytropic Gas scalar fields and dynamics of the scalar fields according to the evolutions of the New Agegraphic Dark Energy, which describes the accelerated expansion of the Universe.

The Fractional View Analysis of Polytropic Gas, Unsteady Flow System

Generally, the differential equations of integer order do not properly model various phenomena in different areas of science and engineering as compared to differential equations of fractional order. The fractional-order differential equations provide the useful dynamics of the physical system and thus provide the innovative and effective information about the given physical system. Keeping in view the above properties of fractional calculus, the present article is related to the analytical solution of the time-fractional system of equations which describe the unsteady flow of polytropic gas dynamics. The present method provides the series form solution with easily computable components and a higher rate of convergence towards the targeted problem’s exact solution. The present techniques are straightforward and effective for dealing with the solutions of fractional-order problems. The fractional derivatives are expressed in terms of the Caputo operator. The targeted problems’ solutions are calculated using the Adomian decomposition method and variational iteration methods along with Shehu transformation. In the current procedures, we first applied the Shehu transform to reduce the problems into a more straightforward form and then implemented the decomposition and variational iteration methods to achieve the problems’ comprehensive results. The solution of the nonlinear equations of unsteady flow of a polytropic gas at various fractional orders of the derivative is the core point of the present study. The solution of the proposed fractional model is plotted via two- and three-dimensional graphs. It is investigated that each problem’s solution-graphs are best fitted with each other and with the exact solution. The convergence of fractional-order problems can be observed towards the solution of integer-order problems. Less computational time is the major attraction of the suggested methods. The present work will be considered a useful tool to handle the solution of fractional partial differential equations.

On invariant finite-difference schemes for equations of one-dimensional flows of a polytropic gas for problems with spatial symmetries

One-dimensional polytropic gas dynamics equations for plane, radially symmetric, and spherically symmetric flows are considered. Invariant properties of equations are discussed, local conservation laws are derived. Additional conservation laws are written, which take place only in case of special values of adiabatic exponent. Classical difference scheme of Samarsky-Popov for gas dynamics has all difference analogs of conservation laws, except for additional ones. In difference schemes additional conservative laws take place in case of special state equation approximation. Scheme of Samarsky-Popov with special state equation was initially suggested by V.A. Korobitsyn. He described it as ‘thermodynamically consistend’ In current paper group properties, and conservation laws of thermodynamically consistent schemes are discussed, and numerical implementation for plane, cylinder, and spherical flows is perfomed.