TY - JOUR
T1 - A length factor artificial neural network method for the numerical solution of the advection dispersion equation characterizing the mass balance of fluid flow in a chemical reactor
AU - Yadav, Neha
AU - McFall, Kevin Stanley
AU - Kumar, Manoj
AU - Kim, Joong Hoon
N1 - Funding Information:
Acknowledgements This work was supported by National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIP) (NRF-2013R1A2A1A01013886) and the Brain Korea 21 (BK-21) fellowship from the Ministry of Education of Korea.
Publisher Copyright:
© 2016, The Natural Computing Applications Forum.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - In this article, a length factor artificial neural network (ANN) method is proposed for the numerical solution of the advection dispersion equation (ADE) in steady state that is used extensively in fluid dynamics and in the mass balance of a chemical reactor. An approximate trial solution of the ADE is constructed in terms of ANN using the concept of the length factor in a way that automatically satisfies the desired boundary conditions, regardless of the ANN output. The mathematical model of ADE is presented adopting a first-order reaction, and the steady-state case for the same is examined by estimating the numerical solution using the ANN technique. Numerical simulations are performed by choosing the best ANN ensemble, based on a combination of numerous design parameters, random starting weights, and biases. The solution obtained using the ANN method is compared to the existing finite difference method (FDM) to test the reliability and effectiveness of the proposed approach. Three cases of ADE are considered in this study for different values of advection and dispersion. The numerical results show that the ANN method exhibits a higher accuracy than the FDM, even for the smaller number of training points in the domain, and eliminates the instability issues for the case where advection dominates dispersion.
AB - In this article, a length factor artificial neural network (ANN) method is proposed for the numerical solution of the advection dispersion equation (ADE) in steady state that is used extensively in fluid dynamics and in the mass balance of a chemical reactor. An approximate trial solution of the ADE is constructed in terms of ANN using the concept of the length factor in a way that automatically satisfies the desired boundary conditions, regardless of the ANN output. The mathematical model of ADE is presented adopting a first-order reaction, and the steady-state case for the same is examined by estimating the numerical solution using the ANN technique. Numerical simulations are performed by choosing the best ANN ensemble, based on a combination of numerous design parameters, random starting weights, and biases. The solution obtained using the ANN method is compared to the existing finite difference method (FDM) to test the reliability and effectiveness of the proposed approach. Three cases of ADE are considered in this study for different values of advection and dispersion. The numerical results show that the ANN method exhibits a higher accuracy than the FDM, even for the smaller number of training points in the domain, and eliminates the instability issues for the case where advection dominates dispersion.
KW - Advection
KW - Artificial neural network
KW - Dispersion
KW - Finite difference method
KW - Steady state
UR - http://www.scopus.com/inward/record.url?scp=85000352365&partnerID=8YFLogxK
U2 - 10.1007/s00521-016-2722-9
DO - 10.1007/s00521-016-2722-9
M3 - Article
AN - SCOPUS:85000352365
SN - 0941-0643
VL - 30
SP - 917
EP - 924
JO - Neural Computing and Applications
JF - Neural Computing and Applications
IS - 3
ER -