Analogue of the mass conservation law for third approximation of one-dimensional nonlinear Boltzmann's moment system equations

2013 ◽  
Vol 54 (5) ◽  
pp. 053512
Author(s):  
A. Sakabekov ◽  
E. Auzhani
Keyword(s):  
Conservation Law ◽  
Mass Conservation ◽  
One Dimensional ◽  
Moment System ◽  
System Equations

scholarly journals Boltzmann’s Six-Moment One-Dimensional Nonlinear System Equations with the Maxwell-Auzhan Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
A. Sakabekov ◽  
Y. Auzhani
Keyword(s):  
Boundary Conditions ◽  
A Priori ◽  
Initial Value ◽  
One Dimensional ◽  
Moment System ◽  
Uniqueness Of The Solution ◽  
System Equations ◽  
Particular Solution ◽  
Integral Equality ◽  
A Priori Estimation

We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.

The Expansion Model of Debris Cloud Induced by Oblique Hypervelocity Impact

2012 ◽  
Vol 13 (3-4) ◽  
Author(s):  
Qing-Ming Zhang ◽  
Y. H. Chen ◽  
F. L. Huang ◽  
Z. Z. Gong
Keyword(s):  
Conservation Law ◽  
Mass Conservation ◽  
Hypervelocity Impact ◽  
Polar Coordinates ◽  
Dynamic Evolution ◽  
Nonlinear Integral Equations ◽  
Simulation Code ◽  
Debris Cloud ◽  
Expansion Model ◽  
Energy Conservation Law

AbstractFor describing the dynamic evolution of debris cloud formed in oblique hypervelocity impact, a model (expressed in polar coordinates) for the shape, the velocity distribution and the mass distribution is developed according to the results of experiments and numerical simulation, and parameters of the Model are identified by nonlinear integral equations which are derived from mass conservation law and energy conservation law. Afterwards, the model has been verified by another simulation code.

scholarly journals Movement of zinc sulphate in a calcium-saturated soil: cation exchange and precipitation of gypsum.

1987 ◽  
Vol 35 (3) ◽  
pp. 295-313
Author(s):  
K. Harmsen
Keyword(s):  
Ion Exchange ◽  
Transition Zone ◽  
Zinc Sulphate ◽  
Solubility Product ◽  
Mass Conservation ◽  
Saturated Soil ◽  
Adsorption Complex ◽  
Dimensional Model ◽  
One Dimensional ◽  
Leaching Solution

A one-dimensional model for the movement of zinc sulphate through calcium-saturated soil is presented. Processes considered include mass flow, ion exchange, precipitation and dissolution. Precipitation occurs when the solubility product of gypsum is exceeded. In the presence of gypsum, ion exchange takes place at two separate interfaces, which move with different velocities through the soil. At the first interface precipitation of gypsum takes place in conjunction with ion exchange, and at the second interface the gypsum dissolves again and ion exchange proceeds until equilibrium is reached with the leaching solution. The composition of the transition zone between the two interfaces is calculated from the conditions of mass conservation and electroneutrality, the solubility product of gypsum and assuming a linear ion exchange equation. It is shown that the concentration of sulphate in the transition zone is higher than in the leaching solution, due to dissolution of gypsum at the second interface. In the presence of gypsum, zinc penetrates deeper into the soil than in its absence, but the fraction of the adsorption complex saturated with zinc is smaller. (Abstract retrieved from CAB Abstracts by CABI’s permission)

scholarly journals High-density compression experiments at ILE, Osaka

1991 ◽  
Vol 9 (2) ◽  
pp. 193-207 ◽  
Author(s):  
H. Azechi ◽  
T. Jitsuno ◽  
T. Kanabe ◽  
M. Katayama ◽  
K. Mima ◽  
...  
Keyword(s):  
Random Phase ◽  
Mass Conservation ◽  
Liquid Density ◽  
Direct Drive ◽  
One Dimensional ◽  
X Ray ◽  
Calculation Results ◽  
Phase Plates ◽  
Thermonuclear Ignition ◽  
Ablated Mass

Direct-drive implosion experiments on the GEKKO XII laser (9 kJ, 0.5 μm, 2 ns) with deuterium and tritium (DT) exchanged plastic hollow shell targets demonstrated fuel areal densities (ρR) of ˜0.1 g/cm2 and fuel densities of ˜600 times liquid density at fuel temperatures of ˜0.3 keV. (The density and ρR values refer only to DT and do not include carbons in the plastic targets.) These values are to be compared with thermonuclear ignition conditions, i.e., fuel densities of 500–1000 times liquid density, fuel areal densities greater than 0.3 g/cm2, and fuel temperatures greater than 5 keV. The irradiation nonuniformity in these experiments was significantly reduced to a level of <5% in root mean square by introducing random-phase plates. The target irregularity was controlled to a 1% level. The fuel ρR was directly measured with the neutron activation of Si, which was originally compounded in the plastic targets. The fuel densities were estimated from the ρR values using the mass conservation relation, where the ablated mass was separately measured using the time-dependent X-ray emission from multilayer targets. Although the observed densities were in agreement with one-dimensional calculation results with convergence ratios of 25–30, the observed neutron yields were significantly lower than those of the calculations. This suggests the implosion uniformity is not sufficient to create a hot spark in which most neutrons should be generated.

A Computational Model for the Study of Gas Turbine Combustor Dynamics

1999 ◽  
Vol 121 (2) ◽  
pp. 243-248 ◽  
Author(s):  
D. M. Costura ◽  
P. B. Lawless ◽  
S. H. Fankel
Keyword(s):  
Gas Turbine ◽  
Mass Conservation ◽  
Single Step ◽  
Combustion Model ◽  
Reacting Flow ◽  
Gas Turbine Combustor ◽  
Splitting Algorithm ◽  
Simulation Code ◽  
One Dimensional ◽  
Engine Simulation

A dynamic combustor model is developed for inclusion into a one-dimensional full gas turbine engine simulation code. A flux-difference splitting algorithm is used to numerically integrate the quasi-one-dimensional Euler equations, supplemented with species mass conservation equations. The combustion model involves a single-step, global finite-rate chemistry scheme with a temperature-dependent activation energy. Source terms are used to account for mass bleed and mass injection, with additional capabilities to handle momentum and energy sources and sinks. Numerical results for cold and reacting flow for a can-type gas turbine combustor are presented. Comparisons with experimental data from this combustor are also made.

scholarly journals AN EQUAL-AREA METHOD FOR SCALAR CONSERVATION LAWS

2011 ◽  
Vol 53 (2) ◽  
pp. 156-170
Author(s):  
MARJETA KRAMAR FIJAVŽ ◽  
MITJA LAKNER ◽  
MARJETA ŠKAPIN RUGELJ
Keyword(s):  
Conservation Law ◽  
Simple Algorithm ◽  
Characteristic Surface ◽  
Scalar Conservation Laws ◽  
Equal Area ◽  
One Dimensional ◽  
Scalar Conservation ◽  
The One ◽  
Integral Version ◽  
Class Of Functions

AbstractWe study the one-dimensional conservation law. We use a characteristic surface to define a class of functions, within which the integral version of the conservation law is solved in a simple and direct way. A simple algorithm for computing the unique solution is developed. The method uses the equal-area principle and yields the solution for any given time directly.

scholarly journals Conservation law modelling of entrainment in layered hydrostatic flows

2015 ◽  
Vol 772 ◽  
pp. 272-294 ◽  
Author(s):  
Paul A. Milewski ◽  
Esteban G. Tabak
Keyword(s):  
Free Surface ◽  
Energy Conservation ◽  
Conservation Law ◽  
Mass Conservation ◽  
Conserved Quantities ◽  
Selection Principle ◽  
Water Flows ◽  
Shallow Water Flows ◽  
The Standard Model ◽  
Upper Boundary

A methodology is developed for modelling entrainment in two-layer shallow water flows using non-standard conserved quantities, replacing layerwise mass conservation by global energy conservation. Thus, the energy that the standard model would regularly dissipate at internal shocks is instead available to exchange fluid between the layers. Two models are considered for the upper boundary of the flow: a rigid lid and a free surface. The latter provides a selection principle for choosing physically relevant conservation laws among the infinitely many that the former possesses, when the ratio between the baroclinic and barotropic speeds tends to zero. Solutions of the equations are studied analytically and numerically, applied to the lock-exchange problem, and compared with other closures.

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