Stability results of a fractional model for unsteady-state fluid flow problem

Abstract

This paper mainly focuses on a fractional model for unsteady-state fluid flow problem developed based on the meshless local Petrov-Galerkin (MLPG) method with the moving kriging (MK) technique as a background. The contribution of this work is to investigate the stability of a model with fractional order governed by the full Navier-Stokes equations in Cartesian coordinate system both theoretical and numerical aspects. This is examined and discussed in detail by means of matrix method. We show that the scheme is unconditionally stable under the restriction of eigenvalue. The dependence between several of the important parameters that impact on the solution is also studied thoroughly. In discretizing the time domain, an algorithm based on a fixed point method is employed to overcome the nonlinearity. Two selected benchmark problems are provided to validate the stability of the present method, and a very satisfactory agreement with the obtained results can be found.