scholarly journals An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena

2018 ◽  
Vol 9 (2) ◽  
pp. 61-75
Author(s):  
Abdelghani Bellouquid ◽  
Jacques Tagoudjeu
Keyword(s):  
Kinetic Equation ◽  
Kinetic Model ◽  
Small Parameter ◽  
Kinetic Models ◽  
Numerical Approach ◽  
Test Cases ◽  
Equivalent Formulation ◽  
Asymptotic Preserving ◽  
Standard Methods ◽  
Asymptotic Preserving Scheme

Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.

scholarly journals An asymptotic preserving scheme for kinetic models with singular limit

2018 ◽  
Vol 11 (4) ◽  
pp. 735-756 ◽  
Author(s):  
Alina Chertock ◽  
◽  
Changhui Tan ◽  
Bokai Yan ◽  
◽  
...  
Keyword(s):  
Kinetic Models ◽  
Singular Limit ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Scheme

scholarly journals Asymptotic preserving scheme for a kinetic model describing incompressible fluids

2015 ◽  
Vol 9 (1) ◽  
pp. 51-74
Author(s):  
Nicolas Crouseilles ◽  
Mohammed Lemou ◽  
SV Raghurama Rao ◽  
Ankit Ruhi ◽  
Muddu Sekhar
Keyword(s):  
Kinetic Model ◽  
Incompressible Fluids ◽  
Asymptotic Preserving ◽  
Asymptotic Preserving Scheme

Asymptotic-Preserving Scheme for the M1-Maxwell System in the Quasi-Neutral Regime

2016 ◽  
Vol 19 (2) ◽  
pp. 301-328 ◽  
Author(s):  
S. Guisset ◽  
S. Brull ◽  
B. Dubroca ◽  
E. d'Humières ◽  
S. Karpov ◽  
...  
Keyword(s):  
Numerical Scheme ◽  
Numerical Test ◽  
Test Cases ◽  
Maxwell System ◽  
Asymptotic Preserving ◽  
Numerical Resolution ◽  
Moment Models ◽  
Asymptotic Preserving Scheme ◽  
The Stability ◽  
Limit Models

AbstractThis work deals with the numerical resolution of the M1-Maxwell system in the quasi-neutral regime. In this regime the stiffness of the stability constraints of classical schemes causes huge calculation times. That is why we introduce a new stable numerical scheme consistent with the transitional and limit models. Such schemes are called Asymptotic-Preserving (AP) schemes in literature. This new scheme is able to handle the quasi-neutrality limit regime without any restrictions on time and space steps. This approach can be easily applied to angular moment models by using a moments extraction. Finally, two physically relevant numerical test cases are presented for the Asymptotic-Preserving scheme in different regimes. The first one corresponds to a regime where electromagnetic effects are predominant. The second one on the contrary shows the efficiency of the Asymptotic-Preserving scheme in the quasi-neutral regime. In the latter case the illustrative simulations are compared with kinetic and hydrodynamic numerical results.

scholarly journals A New Model for the Stochastic Point Reactor: Development and Comparison with Available Models

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 955
Author(s):  
Alamir Elsayed ◽  
Mohamed El-Beltagy ◽  
Amnah Al-Juhani ◽  
Shorooq Al-Qahtani
Keyword(s):  
Kinetic Model ◽  
Differential Equations ◽  
Test Cases ◽  
System Of Differential Equations ◽  
Reactor Model ◽  
Time System ◽  
New Model ◽  
Reactor Dynamics ◽  
Mean And Variance ◽  
The Mean

The point kinetic model is a system of differential equations that enables analysis of reactor dynamics without the need to solve coupled space-time system of partial differential equations (PDEs). The random variations, especially during the startup and shutdown, may become severe and hence should be accounted for in the reactor model. There are two well-known stochastic models for the point reactor that can be used to estimate the mean and variance of the neutron and precursor populations. In this paper, we reintroduce a new stochastic model for the point reactor, which we named the Langevin point kinetic model (LPK). The new LPK model combines the advantages, accuracy, and efficiency of the available models. The derivation of the LPK model is outlined in detail, and many test cases are analyzed to investigate the new model compared with the results in the literature.

Analysis and Modeling of Defects in Unsupported Overhanging Features in Micro-Stereolithography

2016 ◽  
Author(s):  
Vito Basile ◽  
Francesco Modica ◽  
Irene Fassi
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Numerical Approach ◽  
Fe Analysis ◽  
Test Cases ◽  
Layer By Layer ◽  
Failure Condition ◽  
Micro Scale ◽  
Part Geometry ◽  
Shape Component

In the present paper, a numerical approach to model the layer-by-layer construction of cured material during the Additive Manufacturing (AM) process is proposed. The method is developed by a recursive mechanical finite element (FE) analysis and takes into account forces and pressures acting on the cured material during the process, in order to simulate the behavior and investigate the failure condition sources, which lead to defects in the final part geometry. The study is focused on the evaluation of the process capability Stereolithography (SLA), to build parts with challenging features in meso-micro scale without supports. Two test cases, a cantilever part and a bridge shape component, have been considered in order to evaluate the potentiality of the approach. Numerical models have been tuned by experimental test. The simulations are validated considering two test cases and briefly compared to the printed samples. Results show the potential of the approach adopted but also the difficulties on simulation settings.

Model-based analysis of coupled equilibrium-kinetic processes: indirect kinetic studies of thermodynamic parameters using the dynamic data

The Analyst ◽  
2015 ◽  
Vol 140 (9) ◽  
pp. 3121-3135
Author(s):  
Fereshteh Emami ◽  
Marcel Maeder ◽  
Hamid Abdollahi
Keyword(s):  
Kinetic Model ◽  
Thermodynamic Parameters ◽  
Kinetic Models ◽  
Kinetic Studies ◽  
Dynamic Data ◽  
Model Based ◽  
Kinetic Processes ◽  
Model Based Analysis

Schematic of intertwined equilibrium-kinetic model at time = 0,1,2…T when both equilibrium and kinetic models are solved explicitly.

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