Barycentric Rational Collocation Method for the Incompressible Forchheimer Flow in Porous Media

Abstract

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.