Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations
Mathematics and Natural Sciences
The local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the illconditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.
Advances in Applied Mathematics and Mechanics
(2015). Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics, 7(4), 430-440.
Available at: https://aquila.usm.edu/fac_pubs/18789