Abstract
A mixed finite element method (MFEM) stabilized for the two kinds of problems related to the incompressible fluid flow is demonstrated. In the first kind, the Newtonian fluid flow is illustrated with the MFEM and considered discontinuous scheme. Initially, the model equations are considered nonlinear and un-stabilize. The model equations are solved for linear terms with the special technique first and then the model equation with the extra added term is utilized later to stabilize the model equations. A steady-state viscoelastic Oseen fluid flow model with Oldroyd-B type formulations was demonstrated in the second kind of problem with SUPG method. The nonlinear problems are linearized through the Oseen scheme. Numerical results for both the model equations are given and compared. The SUPG method is found more suitable and active.
Highlights
We are interested to discuss only the nonsteady state fluid flow problems under the 2dimensional bounded and connected domain
For the incompressible time independent model equations are standard under applied forces and stresses as follows [1, 2]
The DG method and SU P G method are mostly utilized in viscoelastic fluid flow problems to find the approximate solutions of discontinuous stress strain, In this work, the DG and SUPG methods are used and compared
Summary
We are interested to discuss only the nonsteady state fluid flow problems under the 2dimensional bounded and connected domain. In this case, for the incompressible time independent model equations are standard under applied forces and stresses as follows [1, 2]. Where represents the Wesenberg number which is well known in the given literature and the term ga M. We can write the model equation for given forces f with the given parameter related to the materials as: The model equation for these important issues are given below in detail formulation
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