A Meshless Method based on Moving Kriging Interpolation for the Numerical Solution of the Transient Flow of Magnetohydrodynamic Fractional Maxwell Fluid Equation

Abstract

Maxwell model is one of the most outstanding and widely used models for the description of viscoelastic materials. In this study, we use an efficient meshfree technique based on the Moving Kriging (MK) interpolation for the numerical solution of Magnetohydrodynamic (MHD) flow of fractional Maxwell fluid. In this scheme to discretize this equation in time and space variables, we use the finite difference method and MK interpolation shape functions, respectively. Also, we calculate the local weak form for every node instead of the computation of the global weak form for the global domain. So, we reduce such problems to a system of algebraic equations. To indicate the efficiency of the present scheme, four examples are discussed in various types of domains and with uniform and nonuniform nodal distribution in 2D cases. Also, to show the validity of the method in this example, a comparison with a valid method has been made. Moreover, in the last example, the accuracy of our scheme in the 3D case is illustrated for the fractional telegraph equation.

Keywords

• mhd fractional maxwell fluid
• meshless method
• caputo's fractional derivative
• moving kriging interpolation