2015, 8(1): 45-54. doi: 10.3934/dcdss.2015.8.45

Paralic confinement computations in coastal environment with interlocked areas

1. 

INRIA, Virtual Plants, C.C. 06002, 95 rue de la Galéra, 34095 Montpellier Cedex 5

2. 

Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes

3. 

Inria, Team LEMON, 95 rue de la Galéra, 34090 Montpellier, France

Received  March 2013 Revised  May 2013 Published  July 2014

This paper is in the continuity of a work program, initiated in Frénod & Goubert [4], Frénod & Rousseau [5] and Bernard, Frénod & Rousseau [2]. Its goal is to develop an approach of the paralic confinement usable from the modeling slant, before implementing it in numerical tools.
    More specifically, we here deal with the multiscale aspect of the confinement. If a paralic environment is separated into two (or more) connected areas, we will show that is possible to split the confinement problem into two related problems, one for each area. At the end of this paper, we will focus on the importance of the interface length between the two subdomains.
Citation: Jean-Philippe Bernard, Emmanuel Frénod, Antoine Rousseau. Paralic confinement computations in coastal environment with interlocked areas. Discrete & Continuous Dynamical Systems - S, 2015, 8 (1) : 45-54. doi: 10.3934/dcdss.2015.8.45
References:
[1]

Barnes, A critical appraisal of the application of Guélorget and Pertuisot's concept of the paralic ecosystem and confinement to macrotidal Europe,, Estuarine, 38 (1994), 41.

[2]

J.-P. Bernard, E. Frenod and A. Rousseau, Modeling confinement in Etang de Thau: Numerical simulations and multi-scale aspects,, AIMS Proceedings, ().

[3]

J.-P. Debenay, J.-P. Perthuisot and B. Colleuil, Expression numérique du confinement par les peuplements de foraminifères. App. aux domaines paral. actuels Afri. W.,, C. R. Acad. Sci., 316 (1993), 1823.

[4]

E. Frénod and E. Goubert, A first step towards modelling confinement of paralic ecosystems,, Ecological Modelling, 200 (2007), 139.

[5]

E. Frénod and A. Rousseau, Paralic Confinement: Models and Simulations,, Acta Appl. Math., 123 (2013), 1. doi: 10.1007/s10440-012-9706-2.

[6]

O. Guélorget, G. F. Frisoni and J.-P. Perthuisot, La zonation biologique des milieux lagunaires : Définition d'une échelle de confinement dans le domaine paralique méditérranéen,, Journal de Recherche Océanographique, 8 (1983), 15.

[7]

O. Guélorget, D. Gaujous, M. Louis and J.-P. Perthuisot, Macrobenthofauna of lagoons in guadaloupean mangroves (lesser antilles): Role and expression of confinement,, Journal of Coastal Research, 6 (1990), 611.

[8]

O. Guélorget and J.-P. Perthuisot, Le confinement, paramètre essentiel de la dynamique biologique du domaine paralique,, Sciences Géologiques, 14 (1983), 25.

[9]

O. Guélorget and J.-P. Perthuisot, Le domaine paralique. Expressions géologiques biologique, et économique du confinement,, Presse de l'école normale supérieure 16-1983, (1983), 16.

[10]

L. Halpern, Artificial boundary conditions for the linear advection diffusion equation,, Math. Comp., 46 (1986), 425. doi: 10.1090/S0025-5718-1986-0829617-8.

[11]

, F. Hecht, O. Pironneau and A. Le Hyaric,, FreeFem++ manual., ().

[12]

A. Ibrahim, O. Guélorget, G. G. Frisoni, J. M. Rouchy, A. Martin and J.-P. Perthuisot, Expressions hydrochimiques, biologiques et sédimentologiques des gradients de confinement dans la lagune de guemsah (golfe de suez, egypte),, Oceanologica Acta, 8 (1985), 303.

[13]

J. Poiseuille, Le mouvement des liquides dans les tubes de petits diamètres,, 1844., ().

[14]

F. Redois and J.-P. Debenay, Influence du confinement sur la répartition des foraminifères benthiques : exemples de l'estran d'une ria mésotidale de Bretagne méridionale,, Revue de Paléobiologie, 15 (1996), 243.

[15]

D. Tagliapietra, M. Sigovini and V. Ghirardini, A review of terms and definitions to categorise estuaries, lagoons and associated environments,, Marine and Freshwater Research, 60 (2009), 497. doi: 10.1071/MF08088.

show all references

References:
[1]

Barnes, A critical appraisal of the application of Guélorget and Pertuisot's concept of the paralic ecosystem and confinement to macrotidal Europe,, Estuarine, 38 (1994), 41.

[2]

J.-P. Bernard, E. Frenod and A. Rousseau, Modeling confinement in Etang de Thau: Numerical simulations and multi-scale aspects,, AIMS Proceedings, ().

[3]

J.-P. Debenay, J.-P. Perthuisot and B. Colleuil, Expression numérique du confinement par les peuplements de foraminifères. App. aux domaines paral. actuels Afri. W.,, C. R. Acad. Sci., 316 (1993), 1823.

[4]

E. Frénod and E. Goubert, A first step towards modelling confinement of paralic ecosystems,, Ecological Modelling, 200 (2007), 139.

[5]

E. Frénod and A. Rousseau, Paralic Confinement: Models and Simulations,, Acta Appl. Math., 123 (2013), 1. doi: 10.1007/s10440-012-9706-2.

[6]

O. Guélorget, G. F. Frisoni and J.-P. Perthuisot, La zonation biologique des milieux lagunaires : Définition d'une échelle de confinement dans le domaine paralique méditérranéen,, Journal de Recherche Océanographique, 8 (1983), 15.

[7]

O. Guélorget, D. Gaujous, M. Louis and J.-P. Perthuisot, Macrobenthofauna of lagoons in guadaloupean mangroves (lesser antilles): Role and expression of confinement,, Journal of Coastal Research, 6 (1990), 611.

[8]

O. Guélorget and J.-P. Perthuisot, Le confinement, paramètre essentiel de la dynamique biologique du domaine paralique,, Sciences Géologiques, 14 (1983), 25.

[9]

O. Guélorget and J.-P. Perthuisot, Le domaine paralique. Expressions géologiques biologique, et économique du confinement,, Presse de l'école normale supérieure 16-1983, (1983), 16.

[10]

L. Halpern, Artificial boundary conditions for the linear advection diffusion equation,, Math. Comp., 46 (1986), 425. doi: 10.1090/S0025-5718-1986-0829617-8.

[11]

, F. Hecht, O. Pironneau and A. Le Hyaric,, FreeFem++ manual., ().

[12]

A. Ibrahim, O. Guélorget, G. G. Frisoni, J. M. Rouchy, A. Martin and J.-P. Perthuisot, Expressions hydrochimiques, biologiques et sédimentologiques des gradients de confinement dans la lagune de guemsah (golfe de suez, egypte),, Oceanologica Acta, 8 (1985), 303.

[13]

J. Poiseuille, Le mouvement des liquides dans les tubes de petits diamètres,, 1844., ().

[14]

F. Redois and J.-P. Debenay, Influence du confinement sur la répartition des foraminifères benthiques : exemples de l'estran d'une ria mésotidale de Bretagne méridionale,, Revue de Paléobiologie, 15 (1996), 243.

[15]

D. Tagliapietra, M. Sigovini and V. Ghirardini, A review of terms and definitions to categorise estuaries, lagoons and associated environments,, Marine and Freshwater Research, 60 (2009), 497. doi: 10.1071/MF08088.

[1]

Jean-Philippe Bernard, Emmanuel Frénod, Antoine Rousseau. Modeling confinement in Étang de Thau: Numerical simulations and multi-scale aspects. Conference Publications, 2013, 2013 (special) : 69-76. doi: 10.3934/proc.2013.2013.69

[2]

Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe. Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Mathematical Biosciences & Engineering, 2006, 3 (4) : 571-582. doi: 10.3934/mbe.2006.3.571

[3]

T. J. Newman. Modeling Multicellular Systems Using Subcellular Elements. Mathematical Biosciences & Engineering, 2005, 2 (3) : 613-624. doi: 10.3934/mbe.2005.2.613

[4]

Mats Gyllenberg, Yi Wang. Periodic tridiagonal systems modeling competitive-cooperative ecological interactions. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 289-298. doi: 10.3934/dcdsb.2005.5.289

[5]

Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768

[6]

Zhongkai Guo. Invariant foliations for stochastic partial differential equations with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5203-5219. doi: 10.3934/dcds.2015.35.5203

[7]

Hirotoshi Kuroda, Noriaki Yamazaki. Approximating problems of vectorial singular diffusion equations with inhomogeneous terms and numerical simulations. Conference Publications, 2009, 2009 (Special) : 486-495. doi: 10.3934/proc.2009.2009.486

[8]

Florian De Vuyst, Francesco Salvarani. Numerical simulations of degenerate transport problems. Kinetic & Related Models, 2014, 7 (3) : 463-476. doi: 10.3934/krm.2014.7.463

[9]

Tomás Caraballo, P.E. Kloeden, Pedro Marín-Rubio. Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay. Discrete & Continuous Dynamical Systems - A, 2007, 19 (1) : 177-196. doi: 10.3934/dcds.2007.19.177

[10]

Roberto Camassa, Pao-Hsiung Chiu, Long Lee, W.-H. Sheu. A particle method and numerical study of a quasilinear partial differential equation. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1503-1515. doi: 10.3934/cpaa.2011.10.1503

[11]

Z. Jackiewicz, B. Zubik-Kowal, B. Basse. Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics. Mathematical Biosciences & Engineering, 2009, 6 (3) : 561-572. doi: 10.3934/mbe.2009.6.561

[12]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure & Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017

[13]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116

[14]

Joseph D. Fehribach. Using numerical experiments to discover theorems in differential equations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 495-504. doi: 10.3934/dcdsb.2003.3.495

[15]

Joseph A. Connolly, Neville J. Ford. Comparison of numerical methods for fractional differential equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 289-307. doi: 10.3934/cpaa.2006.5.289

[16]

Nicola Guglielmi, Christian Lubich. Numerical periodic orbits of neutral delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1057-1067. doi: 10.3934/dcds.2005.13.1057

[17]

Roberto Garrappa, Eleonora Messina, Antonia Vecchio. Effect of perturbation in the numerical solution of fractional differential equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2679-2694. doi: 10.3934/dcdsb.2017188

[18]

Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 737-765. doi: 10.3934/dcds.2010.26.737

[19]

Emmanuel Trélat. Optimal control of a space shuttle, and numerical simulations. Conference Publications, 2003, 2003 (Special) : 842-851. doi: 10.3934/proc.2003.2003.842

[20]

Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143-164. doi: 10.3934/mbe.2017010

2017 Impact Factor: 0.561

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (1)

[Back to Top]