scholarly journals A massively parallel exponential integrator for advection-diffusion models

2009 ◽  
Vol 231 (1) ◽  
pp. 82-91 ◽  
Author(s):  
A. Martínez ◽  
L. Bergamaschi ◽  
M. Caliari ◽  
M. Vianello
Keyword(s):  
Diffusion Models ◽  
Massively Parallel ◽  
Advection Diffusion ◽  
Exponential Integrator

scholarly journals A stable numerical method for solving variable coefficient advection–diffusion models

2008 ◽  
Vol 56 (3) ◽  
pp. 754-768 ◽  
Author(s):  
Enrique Ponsoda ◽  
Emilio Defez ◽  
María Dolores Roselló ◽  
José Vicente Romero
Keyword(s):  
Numerical Method ◽  
Variable Coefficient ◽  
Diffusion Models ◽  
Advection Diffusion ◽  
Stable Numerical Method

scholarly journals Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion

2019 ◽  
Vol 150 (5) ◽  
pp. 2322-2348
Author(s):  
Qi Wang ◽  
Jingyue Yang ◽  
Feng Yu
Keyword(s):  
Global Existence ◽  
Elliptic System ◽  
Nonlinear Diffusion ◽  
Uniform Boundedness ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Diffusion Models ◽  
Well Posedness ◽  
Sensitivity Functions ◽  
Advection Diffusion

AbstractThis paper investigates the global well-posedness of a class of reaction–advection–diffusion models with nonlinear diffusion and Lotka–Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic–elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka–Volterra competition systems.

scholarly journals A second order numerical method for solving advection-diffusion models

2009 ◽  
Vol 50 (5-6) ◽  
pp. 806-811 ◽  
Author(s):  
R. Company ◽  
E. Ponsoda ◽  
J.-V. Romero ◽  
M.-D. Roselló
Keyword(s):  
Numerical Method ◽  
Diffusion Models ◽  
Second Order ◽  
Advection Diffusion

The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

2011 ◽  
Vol 680 ◽  
pp. 602-635 ◽  
Author(s):  
R. N. BEARON ◽  
A. L. HAZEL ◽  
G. J. THORN
Keyword(s):  
Random Walk ◽  
Diffusion Model ◽  
Diffusion Models ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Local Flow ◽  
Spatial And Temporal Scales ◽  
Advection Diffusion ◽  
Micro Organisms ◽  
Good Agreement

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection–diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection–diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection–diffusion model to apply. We also use a simple two-dimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the ‘break-down’ regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection–diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

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