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An efficient and accurate fully discrete finite element method for unsteady incompressible Oldroyd fluids with large time step
Author(s) -
Guo Yingwen,
He Yinnian
Publication year - 2015
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4084
Subject(s) - finite element method , compressibility , pressure correction method , incompressible flow , mechanics , mathematics , mathematical analysis , physics , thermodynamics
Summary This paper proposes a second‐order accuracy in time fully discrete finite element method for the Oldroyd fluids of order one. This new approach is based on a finite element approximation for the space discretization, the Crank–Nicolson/Adams–Bashforth scheme for the time discretization and the trapezoid rule for the integral term discretization. It reduces the nonlinear equations to almost unconditionally stable and convergent systems of linear equations that can be solved efficiently and accurately. Here, the numerical simulations for L 2 , H 1 error estimates of the velocity and L 2 error estimates of the pressure at different values of viscoelastic viscosities α , different values of relaxation time λ 1 , different values of null viscosity coefficient μ 0 are shown. In addition, two benchmark problems of Oldroyd fluids with different solvent viscosity μ and different relaxation time λ 1 are simulated. All numerical results perfectly match with the theoretical analysis and show that the developed approach gives a high accuracy to simulate the Oldroyd fluids under a large time step. Furthermore, the difference and the connection between the Newton fluids and the viscoelastic Oldroyd fluids are displayed. Copyright © 2015 John Wiley & Sons, Ltd.