scholarly journals Numerical Simulation of Feller’s Diffusion Equation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1067
Author(s):  
Denys Dutykh
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Fluid Mechanics ◽  
Open Source ◽  
Stability Condition ◽  
Numerical Scheme ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Matlab Code

This article is devoted to Feller’s diffusion equation, which arises naturally in probability and physics (e.g., wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties, we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation, and the corresponding Matlab code is provided with this article under an open source license.

scholarly journals Numerical Simulation of Feller's Diffusion Equation

2019 ◽  
Author(s):  
Denys Dutykh
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Fluid Mechanics ◽  
Open Source ◽  
Stability Condition ◽  
Numerical Scheme ◽  
Turbulence Theory ◽  
Wave Turbulence ◽  
Matlab Code

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

scholarly journals The "step feature" of suprathermal ion distributions: a discriminator between acceleration processes?

2012 ◽  
Vol 30 (9) ◽  
pp. 1315-1319 ◽  
Author(s):  
H. J. Fahr ◽  
H. Fichtner
Keyword(s):  
Numerical Simulation ◽  
Solar Wind ◽  
Diffusion Coefficient ◽  
Power Law ◽  
Analytical Approximation ◽  
The Self ◽  
Wave Turbulence ◽  
Ion Distributions ◽  
Velocity Diffusion ◽  
Suprathermal Particles

Abstract. The discussion of exactly which process is causing the preferred build-up of v−5-power law tails of the velocity distribution of suprathermal particles in the solar wind is still ongoing. Criteria allowing one to discriminate between the various suggestions that have been made would be useful in order to clarify the physics behind these tails. With this study, we draw the attention to the so-called "step feature" of the velocity distributions and offer a criterion that allows one to distinguish between those scenarios that employ velocity diffusion, i.e. second-order Fermi processes, which are prime candidates in the present debate. With an analytical approximation to the self-consistently obtained velocity diffusion coefficient, we solve the transport equation for suprathermal particles. The numerical simulation reveals that this form of the diffusion coefficient naturally leads to the step feature of the velocity distributions. This finding favours – at least in regions of the appearance of the step feature (i.e. for heliocentric distances up to about 11 AU and at lower energies) – the standard velocity diffusion as a consequence of the particle's interactions with the plasma wave turbulence as opposed to that caused by velocity fluctuation-induced compressions and rarefactions.

AN OPEN-SOURCE CODE FOR NUMERICAL SIMULATION OF DRAINAGE BASIN DEVELOPMENT

2017 ◽  
Author(s):  
George H. Shaw ◽  
◽  
Howard D. Mooers ◽  
Josef Smrz ◽  
Zdenek Papez ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Open Source ◽  
Drainage Basin ◽  
Source Code ◽  
Open Source Code ◽  
Basin Development

Hydrocyclone Two Phase Flow Experimental Research Based on Fluid Mechanics

2012 ◽  
Vol 625 ◽  
pp. 117-120
Author(s):  
Hui Xu ◽  
Xiao Hong Chen
Keyword(s):  
Numerical Simulation ◽  
Liquid Phase ◽  
Fluid Mechanics ◽  
Production Capacity ◽  
Phase Flow ◽  
Input Flow ◽  
Two Phase ◽  
Output Flow ◽  
Input Pressure ◽  
Solid Liquid

The liquid phase experiment is finished ,and the relation curve of input- pressure and input-flow、output-flow、distributary rate are worked out.We are bout to calculate the production capacity and define the best distribution rate of the operation parameters.At the same time , the solid-liquid phase separating experiment are made too and we conclude the relation curve of input-pressure and consistency 、separating efficiency .Comparing with the numerical simulation ,the result is reasonable.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals On the Theory of Electron Diffusion in Electrostatic Fields in Gases

1974 ◽  
Vol 27 (2) ◽  
pp. 195 ◽  
Author(s):  
HR Skullerud
Keyword(s):  
Diffusion Coefficient ◽  
Boltzmann Equation ◽  
Diffusion Equation ◽  
Diffusion Tensor ◽  
Lateral Diffusion ◽  
Mean Square ◽  
Electrostatic Fields ◽  
The Mean ◽  
Lateral Diffusion Coefficient

The motion of electrons in a gas in the presence of large electron density gradients has been studied theoretically, starting from the two-term expansion of the Boltzmann equation. The effects of material boundaries have not been considered. An electron swarm released as a b-function in space and with an equilibrium energy distribution is found initially to develop as a spheroid with dimensions determined by the lateral diffusion coefficient. It subsequently passes through a stage involving a slowly decaying pear-shaped deformation, before ultimately becoming an ellipsoid with dimensions determined by the longitudinal and lateral components of the diffusion tensor. Numerical values cited in the literature for the long-term deviations from the mean square widths predicted by the diffusion equation have been found to be in error by factors of 10 or more.

scholarly journals On the Implementation of Open Source CFD System to Flow Visualization in Fluid Mechanics

2020 ◽  
Author(s):  
Ricardo Medina ◽  
Ashkan Motamedi ◽  
Murat Okcay ◽  
B. Oztekin ◽  
Gustavo Menezes ◽  
...  
Keyword(s):  
Fluid Mechanics ◽  
Flow Visualization ◽  
Open Source
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