Open AccessBarycentric Rational Collocation Method for the Incompressible Forchheimer Flow in Porous Media
Author(s) -
QingLi Zhao,
Yongling Cheng
Publication year - 2021
Publication title -
journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.252
H-Index - 13
eISSN - 2314-4785
pISSN - 2314-4629
DOI - 10.1155/2021/5514916
Subject(s) - mathematics , barycentric coordinate system , collocation (remote sensing) , collocation method , incompressible flow , compressibility , numerical analysis , porous medium , rate of convergence , flow (mathematics) , convergence (economics) , mathematical analysis , geometry , mechanics , porosity , computer science , ordinary differential equation , channel (broadcasting) , physics , geotechnical engineering , computer network , machine learning , economic growth , engineering , economics , differential equation
Barycentric rational collocation method is introduced to solve the Forchheimer law modeling incompressible fluids in porous media. The unknown velocity and pressure are approximated by the barycentric rational function. The main advantages of this method are high precision and efficiency. At the same time, the algorithm and program can be expanded to other problems. The numerical stability can be guaranteed. The matrix form of the collocation method is obtained from the discrete numerical schemes. Numerical analysis and error estimates for velocity and pressure are established. Numerical experiments are carried out to validate the convergence rates and show the efficiency.