Shock Structure and Temperature Overshoot in Macroscopic Model of Mixtures

2015 ◽  
pp. 339-349 ◽  
Author(s):  
Tommaso Ruggeri ◽  
Masaru Sugiyama
Keyword(s):  
Shock Structure ◽  
Macroscopic Model

scholarly journals Vertical Structure of Spiral Shocks in a Corrugated Galactic Disc

1983 ◽  
Vol 100 ◽  
pp. 145-146
Author(s):  
A. H. Nelson ◽  
T. Matsuda ◽  
T. Johns
Keyword(s):  
Density Profile ◽  
Vertical Velocity ◽  
Gas Flow ◽  
Vertical Structure ◽  
Vertical Motion ◽  
Shock Structure ◽  
Galactic Disc ◽  
Gaussian Density ◽  
Abundant Evidence ◽  
Steady Shock

Numerical calculations of spiral shocks in the gas discs of galaxies (1,2,3) usually assume that the disc is flat, i.e. the gas motion is purely horizontal. However there is abundant evidence that the discs of galaxies are warped and corrugated (4,5,6) and it is therefore of interest to consider the effect of the consequent vertical motion on the structure of spiral shocks. If one uses the tightly wound spiral approximation to calculate the gas flow in a vertical cut around a circular orbit (i.e the ⊝ -z plane, see Nelson & Matsuda (7) for details), then for a gas disc with Gaussian density profile in the z-direction and initially zero vertical velocity a doubly periodic spiral potential modulation produces the steady shock structure shown in Fig. 1. The shock structure is independent of z, and only a very small vertical motion appears with anti-symmetry about the mid-plane.

scholarly journals Shock Structure and Relaxation in the Multi-Component Mixture of Euler Fluids

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 955
Author(s):  
Damir Madjarević ◽  
Milana Pavić-Čolić ◽  
Srboljub Simić
Keyword(s):  
Relaxation Times ◽  
Thermal Relaxation ◽  
Collision Operator ◽  
Weak Form ◽  
Shock Structure ◽  
Theory Approach ◽  
Component Mixture ◽  
Single Temperature ◽  
The Difference ◽  
Euler Fluids

The shock structure problem is studied for a multi-component mixture of Euler fluids described by the hyperbolic system of balance laws. The model is developed in the framework of extended thermodynamics. Thanks to the equivalence with the kinetic theory approach, phenomenological coefficients are computed from the linearized weak form of the collision operator. Shock structure is analyzed for a three-component mixture of polyatomic gases, and for various combinations of parameters of the model (Mach number, equilibrium concentrations and molecular mass ratios). The analysis revealed that three-component mixtures possess distinguishing features different from the binary ones, and that certain behavior may be attributed to polyatomic structure of the constituents. The multi-temperature model is compared with a single-temperature one, and the difference between the mean temperatures of the mixture are computed. Mechanical and thermal relaxation times are computed along the shock profiles, and revealed that the thermal ones are smaller in the case discussed in this study.

MICRO AND MESO SCALES OF DESCRIPTION CORRESPONDING TO A MODEL OF TISSUE INVASION BY SOLID TUMOURS

2005 ◽  
Vol 15 (11) ◽  
pp. 1667-1683 ◽  
Author(s):  
MIROSŁAW LACHOWICZ
Keyword(s):  
Mathematical Models ◽  
Type Equation ◽  
Reaction Diffusion ◽  
Solid Tumours ◽  
Macroscopic Model ◽  
Scale Level ◽  
Micro Scale ◽  
Tissue Invasion ◽  
Mathematical Relationships ◽  
Meso Scale

In this paper two new mathematical models are proposed that correspond to a macroscopic model of tissue invasion of solid tumours, in terms of a system of reaction-diffusion-chemotaxis equations. The first model is defined at the micro-scale level of a large number of interacting individual entities, and is in terms of a linear (Markov) equation. The second model refers to the meso-scale level of description of test-entities and is given in terms of a bilinear Boltzmann-type equation. Mathematical relationships among these three possible descriptions are formulated. Explicit error estimates are given.

MIXED CONFORMING ELEMENTS FOR THE LARGE-BODY LIMIT IN MICROMAGNETICS

2013 ◽  
Vol 24 (01) ◽  
pp. 113-144 ◽  
Author(s):  
MARKUS AURADA ◽  
JENS M. MELENK ◽  
DIRK PRAETORIUS
Keyword(s):  
Mixed Finite Element ◽  
Large Body ◽  
Mixed Finite Element Method ◽  
Adaptive Strategy ◽  
Posteriori Error ◽  
Higher Order ◽  
Three Dimensions ◽  
Macroscopic Model ◽  
Error Estimator ◽  
Discrete Problem

We introduce a stabilized conforming mixed finite element method for a macroscopic model in micromagnetics. We show well-posedness of the discrete problem for higher order elements in two and three dimensions, develop a full a priori analysis for lowest order elements, and discuss the extension of the method to higher order elements. We introduce a residual-based a posteriori error estimator and present an adaptive strategy. Numerical examples illustrate the performance of the method.

Shock structure for heat conducting and viscid fluids

Meccanica ◽  
1981 ◽  
Vol 16 (3) ◽  
pp. 149-156 ◽  
Author(s):  
A. M. Anile ◽  
A. Majorana
Keyword(s):  
Shock Structure ◽  
Heat Conducting

Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet

2001 ◽  
Vol 105 (1043) ◽  
pp. 9-16 ◽  
Author(s):  
S. B. Verma ◽  
E. Rathakrishnan
Keyword(s):  
Mach Number ◽  
Fundamental Frequency ◽  
Acoustic Field ◽  
Major Axis ◽  
Shock Structure ◽  
Minor Axis ◽  
Noise Levels ◽  
Underexpanded Jets ◽  
Barrel Shock ◽  
Mach Numbers

Abstract The shock-structure and the related acoustic field of underexpanded jets undergoes significant changes as the Mach number Mj is increased. The present investigation is carried out to study the effect of Mach number on an underexpanded 2:1 elliptic-slot jet. Experimental data are presented for fully expanded Mach numbers ranging from 1.3 to 2.0. It is observed that the ‘cross-over’ point at the end of the first cell at low Mach numbers gets replaced by a normal shock at a highly underexpanded condition resulting in the formation of a ‘barrel’ shock along the minor-axis side with a ‘bulb’ shock formed along the major-axis side. The above change in shock structure is accompanied by a related change in the acoustic field. The amplitude of fundamental frequency along the minor-axis side grows with Mj but falls beyond Mj = 1.75. Along the major-axis side, however, the fundamental frequency does not exist at low Mach numbers. It appears at Mj = 1.75 but then falls at Mj = 2.0. The related azimuthal directivity of overall noise levels (OASPL) shows significant changes with Mj.

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