Localized method of approximate particular solutions for solving unsteady Navier-Stokes problem

The localized method of approximate particular solutions (LMAPS) is proposed to solve two-dimensional transient incompressible Navier-Stokes systems of equations in primitive variables. The equations contain the Laplacian operator. In avoiding ill-conditioning problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear system within local supporting domain in which five nearest neighboring points and multiquadrics are used for interpolation. Then local matrices are reformulated in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The method is assessed on driven cavity problem and flow around cylinder. The numerical experiments show that the newly developed LMAPS is suitable for solving incompressible Navier-Stokes equations with high accuracy and efficiency.