Numerical Solution of the Compressible Boundary-Layer Equations Using the Finite Element Method

AIAA Journal ◽  
1993 ◽  
Vol 31 (1) ◽  
pp. 6-7 ◽  
Author(s):  
E. Hytopoulos ◽  
J. A. Schetz ◽  
M. Gunzburger
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Compressible Boundary Layer ◽  
The Finite Element Method ◽  
Boundary Layer Equations ◽  
Element Method

Numerical Solution of the Incompressible Boundary-Layer Equations Using the Finite Element Method

1992 ◽  
Vol 114 (4) ◽  
pp. 504-511 ◽  
Author(s):  
J. A. Schetz ◽  
E. Hytopoulos ◽  
M. Gunzburger
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Memory Storage ◽  
The Finite Element Method ◽  
Boundary Layer Equations ◽  
Numerical Predictions ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary ◽  
Element Method

A new approach to the solution of the two-dimensional, incompressible, boundary-layer equations based on the Finite Element Method in both directions is investigated. Earlier Finite Element Method treatments of parabolic boundary-layer problems used finite differences in the streamwise direction, thus sacrificing some of the possible advantages of the Finite Element Method. The accuracy and computational efficiency of different interpolation functions for the velocity field are evaluated. A new element especially designed for boundary layer flows is introduced. The effect that the treatment of the continuity equation has on the stability and accuracy of the numerical results is also discussed. The parabolic nature of the equations is exploited in order to reduce the memory requirements. The solution is obtained for one line at a time, thus only two levels are required to be stored at any time. Efficient solvers for tridiagonal and pentadiagonal forms are used for solving the resulting matrix problem. Numerical predictions are compared to analytical and experimental results for laminar and turbulent flows, with and without pressure gradients. The comparisons show very good agreement. Although most of the cases were tested on a mainframe, the low requirements in CPU time and memory storage allows the implementation of the method on a conventional PC.

Stratification and Buoyancy Effect of Heat Transportation in Magnetohydrodynamics Micropolar Fluid Flow Passing Over a Porous Shrinking Sheet Using the Finite Element Method

2019 ◽  
Vol 8 (8) ◽  
pp. 1640-1647 ◽  
Author(s):  
Shahid Ali Khan ◽  
Yufeng Nie ◽  
Bagh Ali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Mesh Size ◽  
Stratified Medium ◽  
Shrinking Sheet ◽  
The Finite Element Method ◽  
Nonlinear Odes ◽  
Micropolar Fluid Flow ◽  
Element Method

The current study investigates the numerical solution of steady heat transportation in magnetohydrodynamics flow of micropolar fluids over a porous shrinking/stretching sheet with stratified medium and buoyancy force. Based on similarity transformation, the partial differential governing equations are assimilated into a set of nonlinear ODEs, which are numerically solved by the finite element method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising thermophysical parameters namely, suction, magnetic, stratification, heat source, and buoyancy parameter. Under the limiting case, the numerical solution of the velocity and temperature is compared with present work. Better consistency between the two sets of solutions was determined. To verify the convergence of the numerical solution, the calculation is made by reducing the mesh size. The present study finds applications in materials processing and demonstrates convergence characteristics for the finite element method code.

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