scholarly journals A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 453 ◽  
Author(s):  
Mukhtar ◽  
Sohaib ◽  
Ahmad
Keyword(s):  
Numerical Approximation ◽  
Chemical Engineering ◽  
Numerical Study ◽  
Moment Generating Function ◽  
Numerical Approach ◽  
Test Problems ◽  
Batch Crystallization ◽  
One Dimensional ◽  
Engineering Sciences ◽  
The Moment

In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.

scholarly journals On the first hitting place of the integrated Wiener process

1989 ◽  
Vol 21 (4) ◽  
pp. 945-948 ◽  
Author(s):  
Mario Lefebvre ◽  
Éric Léonard
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
Moment Generating Function ◽  
One Dimensional ◽  
The Moment

Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (1) ◽  
pp. 175-184 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a > 0 or −b < 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals First Passage Problems for Asymmetric Wiener Processes

2006 ◽  
Vol 43 (01) ◽  
pp. 175-184
Author(s):  
Mario Lefebvre
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
Expected Value ◽  
First Passage ◽  
One Dimensional ◽  
Wiener Processes ◽  
The Moment

The problem of computing the moment generating function of the first passage time T to a &gt; 0 or −b &lt; 0 for a one-dimensional Wiener process {X(t), t ≥ 0} is generalized by assuming that the infinitesimal parameters of the process may depend on the sign of X(t). The probability that the process is absorbed at a is also computed explicitly, as is the expected value of T.

scholarly journals Evaluating the Capability of the Flux-Limiter Schemes in Capturing Strong Shocks and Discontinuities

2013 ◽  
Vol 20 (2) ◽  
pp. 287-296 ◽  
Author(s):  
Iman Harimi ◽  
Ahmad Reza Pishevar
Keyword(s):  
Numerical Study ◽  
Wave Interaction ◽  
Numerical Code ◽  
Test Problems ◽  
Governing Equations ◽  
Tvd Schemes ◽  
One Dimensional ◽  
Flux Limiter ◽  
Acoustic Interaction ◽  
Density Disturbance

A numerical study is conducted to investigate the capability of the flux-limiter TVD schemes in capturing sharp discontinuities like shock waves. For this purpose, four classical test problems are considered such as slowly moving shock, gas Riemann problem with high density and pressure ratios, shock wave interaction with a density disturbance and shock-acoustic interaction. The governing equations consist of one-dimensional and quasi-one-dimensional Euler equations solved using an in-house numerical code. In order to validate the solution, the obtained results are compared with other results found in the literature.

scholarly journals On the first hitting place of the integrated Wiener process

1989 ◽  
Vol 21 (04) ◽  
pp. 945-948
Author(s):  
Mario Lefebvre ◽  
Éric Léonard
Keyword(s):  
Wiener Process ◽  
Generating Function ◽  
Moment Generating Function ◽  
One Dimensional ◽  
The Moment

Let dx(t) = y(t) dt, where y(t) is a one-dimensional Wiener process. In this note, we obtain a formula for the moment-generating function of y(T), where T is the 1/2-winding time about the origin of the integrated Wiener process x(t).

Some remarks on the Rayleigh process

1986 ◽  
Vol 23 (2) ◽  
pp. 398-408 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Time Problem ◽  
The Moment ◽  
First Passage Time Problem ◽  
Rayleigh Process ◽  
Absorption Condition

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

Some remarks on the Rayleigh process

1986 ◽  
Vol 23 (02) ◽  
pp. 398-408 ◽  
Author(s):  
V. Giorno ◽  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
First Passage Time ◽  
Moment Generating Function ◽  
Passage Time ◽  
First Passage ◽  
One Dimensional ◽  
Time Problem ◽  
The Moment ◽  
First Passage Time Problem ◽  
Rayleigh Process ◽  
Absorption Condition

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

One-dimensional numerical study of compressible flow ejector

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1469-1472
Author(s):  
S. Han ◽  
J. Peddieson
Keyword(s):  
Compressible Flow ◽  
Numerical Study ◽  
One Dimensional

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

Investigation of two-dimensional nonstationary processes of outflow a gas-saturated liquid from axisymmetric vessels

2012 ◽  
Vol 9 (1) ◽  
pp. 47-52
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Buzina
Keyword(s):  
Comparative Analysis ◽  
Numerical Model ◽  
Liquid Mixture ◽  
Phase Model ◽  
Test Problems ◽  
Two Dimensional ◽  
Nonstationary Processes ◽  
Saturated Liquid ◽  
Two Phase ◽  
One Dimensional

The two-dimensional and two-phase model of the gas-liquid mixture is constructed. The validity of numerical model realization is justified by using a comparative analysis of test problems solution with one-dimensional calculations. The regularities of gas-saturated liquid outflow from axisymmetric vessels for different geometries are established.

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