Evolution of weak discontinuity waves in self-similar flows and formation of secondary shocks. The ?point explosion model?

1982 ◽  
Vol 33 (1) ◽  
pp. 63-80 ◽  
Author(s):  
N. Virgopia ◽  
F. Ferraioli
Keyword(s):  
Weak Discontinuity ◽  
Point Explosion ◽  
Discontinuity Waves ◽  
Self Similar ◽  
Similar Flows

Comparison of the numerical and self-similar solutions of Sedov’s problem on a point explosion in gas

2020 ◽  
Vol 15 (3-4) ◽  
pp. 212-216
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Gas Dynamics ◽  
Numerical Solutions ◽  
Similarity Theory ◽  
Compressible Medium ◽  
Initial Moment ◽  
Point Explosion ◽  
Perfect Gas ◽  
Gas Dynamics Equations ◽  
Self Similar ◽  
Similar Solutions

Comparative analysis of solutions of Sedov’s problem of a point explosion in gas for the plane case, obtained by the analytical method and using the open software package of computational fluid dynamics OpenFOAM, is carried out. A brief analysis of methods of dimensionality and similarity theory used for the analytical self-similar solution of point explosion problem in a perfect gas (nitrogen) which determined by the density of uncompressed gas, magnitude of released energy, ratio of specific heat capacities and by the index of geometry of the explosion is given. The system of one-dimensional gas dynamics equations for a perfect gas includes the laws of conservation of mass, momentum, and energy is used. It is assumed that at the initial moment of time there is a point explosion with instantaneous release of energy. Analytical self-similar solutions for the Euler and Lagrangian coordinates, mass velocity, pressure, temperature, and density in the case of plane geometry are given. The numerical simulation of considered process in sonicFoam solver of OpenFOAM package built on the PISO algorithm was performed. For numerical modeling the system of differential equations of gas dynamics is used, including the equations of continuity, Navier-Stokes motion for a compressible medium and conservation of internal energy. Initial and boundary conditions were selected in accordance with the obtained analytical solution using the setFieldsDict, blockMeshDict, and uniformFixedValue utilities. The obtained analytical and numerical solutions have a satisfactory agreement.

Rotational λ – hypersurfaces in Euclidean spaces

2021 ◽  
Vol 30 (1) ◽  
pp. 29-40
Author(s):  
KADRI ARSLAN ◽  
ALIM SUTVEREN ◽  
BETUL BULCA
Keyword(s):  
Present Article ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Special Solution ◽  
Euclidean Spaces ◽  
Self Similar ◽  
The Mean ◽  
Similar Flows

Self-similar flows arise as special solution of the mean curvature flow that preserves the shape of the evolving submanifold. In addition, \lambda -hypersurfaces are the generalization of self-similar hypersurfaces. In the present article we consider \lambda -hypersurfaces in Euclidean spaces which are the generalization of self-shrinkers. We obtained some results related with rotational hypersurfaces in Euclidean 4-space \mathbb{R}^{4} to become self-shrinkers. Furthermore, we classify the general rotational \lambda -hypersurfaces with constant mean curvature. As an application, we give some examples of self-shrinkers and rotational \lambda -hypersurfaces in \mathbb{R}^{4}.

scholarly journals Mathematical Theory of Cylindrical Isothermal Blast Waves in a Magnetic Field

1981 ◽  
Vol 34 (3) ◽  
pp. 279 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Supernova Remnants ◽  
Magnetic Pressure ◽  
Blast Waves ◽  
Physical Domain ◽  
Fluid Flow Velocity ◽  
Magnetic Tension ◽  
Self Similar ◽  
The Magnetic Field ◽  
Similar Flows

An investigation is made of the self-similar flow behind a cylindrical blast wave from a line explosion (situated on r = 0, using conventional cylindrical coordinates r, 4>, z) in a medium whose density and magnetic field both vary as r -w ahead of the blast front, with the assumption that the flow is isothermal. The magnetic field can have components in both the azimuthal B(jJ and longitudinal B, directions. It is found that: (i) For B(jJ =f:. 0 =f:. B, a continuous single-valued solution with a velocity field representing outflow of material away from the line of explosion does not exist for OJ OJ > 0 the governing equation possesses a set of movable critical points. In this case it is shown that the fluid flow velocity is bracketed between two curves and that the asymptotes of the velocity curve on the shock are intersected by, or are tangent to, the two curves. Thus a solution always exists in the physical domain r ~ o. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results have an impact upon previous applications of the theory of self-similar flows to evolving supernova remnants without allowance for the dynamical influence of magnetic pressure and magnetic tension.

Self-similar flows with increasing energy—2. Isothermal flow

1972 ◽  
Vol 10 (11) ◽  
pp. 963-973 ◽  
Author(s):  
Melam P. Ranga Rao ◽  
Sharad C. Purohit
Keyword(s):  
Isothermal Flow ◽  
Self Similar ◽  
Similar Flows

Self-similar, time-dependent flows with a free surface

1976 ◽  
Vol 73 (4) ◽  
pp. 603-620 ◽  
Author(s):  
Michael S. Longuet-Higgins
Keyword(s):  
Free Surface ◽  
Rational Functions ◽  
Rigid Wall ◽  
The Other ◽  
Three Dimensions ◽  
Simple Derivation ◽  
Similar Time ◽  
Self Similar ◽  
Parabolic Flow ◽  
Similar Flows

A simple derivation is given of the parabolic flow first described by John (1953) in semi-Lagrangian form. It is shown that the scale of the flow decreases liket−3, and the free surface contracts about a point which lies one-third of the way from the vertex of the parabola to the focus.The flow is an exact limiting form of either a Dirichlet ellipse or hyperbola, as the timettends to infinity.Two other self-similar flows, in three dimensions, are derived. In one, the free surface is a paraboloid of revolution, which contracts liket−2about a point lying one-quarter the distance from the vertex to the focus. In the other, the flow is non-axisymmetric, and the free surface contracts liket−5.The parabolic flow is shown to be one of a general class of self-similar flows in the plane, described by rational functions of degreen. The parabola corresponds ton= 2. Whenn= 3 there are two new flows. In one of these the scale varies ast12/7and the free surface has the appearance of a trough filling up. In the other, the free surface resembles flow round the end of a rigid wall; the scale varies ast−4·17.

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