Abstract:
In this paper, we present a numerical scheme used to solve the nonlinear time fractional Navier–Stokes equations in two dimensions. We first employ the meshless local
Petrov–Galerkin (MLPG) method based on a local weak formulation to form the system
of discretized equations and then we will approximate the time fractional derivative
interpreted in the sense of Caputo by a simple quadrature formula. The moving Kriging
interpolation which possesses the Kronecker delta property is applied to construct
shape functions. This research aims to extend and develop further the applicability of
the truly MLPG method to the generalized incompressible Navier–Stokes equations.
Two numerical examples are provided to illustrate the accuracy and efficiency of the
proposed algorithm. Very good agreement between the numerically and analytically
computed solutions can be observed in the verification. The present MLPG method
has proved its efficiency and reliability for solving the two-dimensional time fractional
Navier–Stokes equations arising in fluid dynamics as well as several other problems in
science and engineering.