American Institute of Mathematical Sciences

Advanced
March  2010, 13(2): 489-501. doi: 10.3934/dcdsb.2010.13.489

On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer

Xiaoming Wang 1,

1. 

Department of Mathematics, Florida State University, Tallahassee, FL32306

Received  September 2009 Revised  October 2009 Published  December 2009

We show that the coupled continuum pipe flow model (CCPF) for flows in karst aquifers is ill-posed in the sense that no reasonable solution exists. We also demonstrate that Hua's modified CCPF model is ill-posed in 3D although it is well-posed in two spatial dimensions. A new modification of the original CCPF model that is consistent with basic physics is proposed and its well-posedness is proved here. We believe that this is the first physically relevant well-posed CCPF type model in 3D.
Keywords: existence of solution., conduit flow process (CFP), Hua's modified CCPF model, karst aquifer, original and modified coupled continuum pipe-flow model (CCPF).
Mathematics Subject Classification: Primary: 86A05, 35Q35; Secondary: 76D03, 86A99, 76S0.
Citation: Xiaoming Wang. On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 489-501. doi: 10.3934/dcdsb.2010.13.489
[1]

Joachim Naumann, Jörg Wolf. On Prandtl's turbulence model: Existence of weak solutions to the equations of stationary turbulent pipe-flow. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1371-1390. doi: 10.3934/dcdss.2013.6.1371
[2]

Fabian Rüffler, Volker Mehrmann, Falk M. Hante. Optimal model switching for gas flow in pipe networks. Networks & Heterogeneous Media, 2018, 13 (4) : 641-661. doi: 10.3934/nhm.2018029
[3]

Theodore Tachim Medjo. On the convergence of a stochastic 3D globally modified two-phase flow model. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 395-430. doi: 10.3934/dcds.2019016
[4]

Pierre Aime Feulefack, Jean Daniel Djida, Atangana Abdon. A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3227-3247. doi: 10.3934/dcdsb.2018317
[5]

Theodore Tachim Medjo. Pullback $ \mathbb{V}-$attractor of a three dimensional globally modified two-phase flow model. Discrete & Continuous Dynamical Systems, 2018, 38 (4) : 2141-2169. doi: 10.3934/dcds.2018088
[6]

Zengji Du, Zhaosheng Feng. Existence and asymptotic behaviors of traveling waves of a modified vector-disease model. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1899-1920. doi: 10.3934/cpaa.2018090
[7]

Jonathan Zinsl. The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 919-933. doi: 10.3934/dcdss.2017047
[8]

Wenzhang Huang. Weakly coupled traveling waves for a model of growth and competition in a flow reactor. Mathematical Biosciences & Engineering, 2006, 3 (1) : 79-87. doi: 10.3934/mbe.2006.3.79
[9]

Roberto Garra. Confinement of a hot temperature patch in the modified SQG model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2407-2416. doi: 10.3934/dcdsb.2018258
[10]

Xiao He, Sining Zheng. Protection zone in a modified Lotka-Volterra model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2027-2038. doi: 10.3934/dcdsb.2015.20.2027
[11]

Yves Coudière, Anđela Davidović, Clair Poignard. Modified bidomain model with passive periodic heterogeneities. Discrete & Continuous Dynamical Systems - S, 2020, 13 (8) : 2231-2258. doi: 10.3934/dcdss.2020126
[12]

Micol Amar, Daniele Andreucci, Claudia Timofte. Homogenization of a modified bidomain model involving imperfect transmission. Communications on Pure & Applied Analysis, 2021, 20 (5) : 1755-1782. doi: 10.3934/cpaa.2021040
[13]

Maolin Cheng, Bin Liu. Application of a modified VES production function model. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2889-2902. doi: 10.3934/jimo.2020099
[14]

Esther S. Daus, Josipa-Pina Milišić, Nicola Zamponi. Global existence for a two-phase flow model with cross-diffusion. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 957-979. doi: 10.3934/dcdsb.2019198
[15]

Hua Qiu, Shaomei Fang. A BKM's criterion of smooth solution to the incompressible viscoelastic flow. Communications on Pure & Applied Analysis, 2014, 13 (2) : 823-833. doi: 10.3934/cpaa.2014.13.823
[16]

Jacek Polewczak, Ana Jacinta Soares. On modified simple reacting spheres kinetic model for chemically reactive gases. Kinetic & Related Models, 2017, 10 (2) : 513-539. doi: 10.3934/krm.2017020
[17]

Maolin Cheng, Mingyin Xiang. Application of a modified CES production function model based on improved firefly algorithm. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1571-1584. doi: 10.3934/jimo.2019018
[18]

Najwa Najib, Norfifah Bachok, Norihan Md Arifin, Fadzilah Md Ali. Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model. Numerical Algebra, Control & Optimization, 2019, 9 (4) : 423-431. doi: 10.3934/naco.2019041
[19]

Keisuke Takasao. Existence of weak solution for mean curvature flow with transport term and forcing term. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2655-2677. doi: 10.3934/cpaa.2020116
[20]

Sergey A. Suslov. Two-equation model of mean flow resonances in subcritical flow systems. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 165-176. doi: 10.3934/dcdss.2008.1.165

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (53)
  • HTML views (0)
  • Cited by (18)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences