Abstract
The least-squares finite element method (LSFEM) is successfully employed for the discretization of the Stokes equations and the numerical computation of the behaviour of two-dimensional Stokes flow in a straight rectangular channel under the effect of a point-source magnetic field. LSFEM has several advantages in terms of theory and computing, where it can always create a symmetric, positive-definite algebraic system of equations. It also allows for using an equal order shape function for both velocity and pressure, and it is not required to satisfy the Ladyzhenskaya–Babuška–Brezzi (LBB) condition. Despite this, LSFEM has an issue where low-order nodal expansions tend to lock. Thus, the present study proposes the discretization of the problem domain using higher-order nodes elements with full numerical integration. Results concerning velocity contour and streamlines pattern are shown. On the basis of current findings, it can be concluded that the LSFEM can be used to solve Stokes flow problem under the point source magnetic field.
Highlights
Stokes flow is incompressible viscous flow in slow motion
This study proposes least-squares finite element method (LSFEM) for solving Stokes flow subjected to a point-source
Stokesequation equationwith with a point-source magnetic using the least-squares finite element method
Summary
Stokes flow is incompressible viscous flow in slow motion. Stokes flow has numerous crucial functions in industries such as medical applications, the design of innovative materials, lab-on-chip technologies, microdevices, and biological systems. They utilized a square cavity with a moving top lid with constant velocity, and solved this problem using the dual reciprocity boundary element method (DRBEM). They came up with an iterative DRBEM for solving the Stokes flow problem by adding another model problem, a circular cavity [3]. In the study by [4], the two-dimensional Stokes flow problem was solved by developing the analytical method of superposition. The authors in [5] used vorticity–velocity formulation in combination with the multiquadric method (MQ) to handle steady-state Stokes flow problems in 2D and 3D.
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