Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations (Advances in Applied Mathematics and Mechanics, 2018)
The local RBFs based collocation methods (LRBFCM) is presented tosolve two-dimensional incompressible Navier-Stokes equations. In avoiding the ill-conditionedproblem, the weight coefficients of linear combination with respect to thefunction values and its derivatives can be obtained by solving low-order linear systemswithin local supporting domain. Then, we reformulate local matrix in the global andsparse matrix. The obtained large sparse linear systems can be directly solved insteadof using more complicated iterative method. The numerical experiments have shownthat the developed LRBFCM is suitable for solving the incompressible Navier-Stokesequations with high accuracy and efficiency.