The development of power-law preconditioning approach for simulation of unsteady viscoelastic flows

One of the unique features of viscoelastic fluids in unsteady flows is the damping oscillatory behavior without using oscillation and external force, the cause of this is the elastic feature of these fluids. In this essay, the power-law preconditioning method of local stress sensors is used for the first time, to solve the numerical solutions of unsteady flows of viscoelastic fluid while passing through two fixed parallel planes. The Maxwell's equations have been used for this simulation. In this method, by adding a false time derivative to the governing equations, the formation of equations become hyperbola (artificial compressibility). By acquiring the preconditioning matrix of these equations that are corrected from the relationship between stress fields, solving unsteady incompressible flow equations as artificial compressible, is possible when using a dual-time algorithm that contains inner and external cordon. For convergence of inner cordon , Vossougi Far’s four-step numerical method is used. For discretization of equations, the first-order finite difference and second-order finite difference are used. The calculations of unsteady flows of viscoelastic fluid for Reynolds numbers, Weissenberg numbers and various passive viscosity ratio, are presented. These results are similar to numerical results. The convergence rate results show that the power-law preconditioned method of local stress sensor for a viscosity ratio of less than 0.5 for high stability, increase the convergence speed and reduce the cost of calculations.