Finite-Element Methods for the Streamfunction-Vorticity Equations: Boundary-Condition Treatments and Multiply Connected Domains

1988 ◽  
Vol 9 (4) ◽  
pp. 650-668 ◽  
Author(s):  
Max D. Gunzburger ◽  
Janet S. Peterson
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Finite Element Methods ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Vorticity Equations

Shape Interrogation by Medial Axis Transform

1990 ◽  
Author(s):  
N. M. Patrikalakis ◽  
H. N. Gursoy
Keyword(s):  
Finite Element ◽  
Medial Axis ◽  
Multiply Connected Domains ◽  
Medial Axis Transform ◽  
Curved Boundaries ◽  
Multiply Connected ◽  
Maximum Thickness ◽  
Surface Patches ◽  
Geometric Representations ◽  
Shape Characteristics

Abstract In this paper we develop a new interrogation method based on the medial axis transform to extract some important global shape characteristics from geometric representations. These shape characteristics include constrictions, maximum thickness points, and associated length scales; isolation of holes and their proximity information; and a set of topologically simple subdomains decomposing a complex domain. The algorithm we develop to compute the medial axis transform of planar multiply connected shapes with curved boundaries can automatically identify these characteristics. Higher level algorithms for generation of finite element meshes of planar multiply connected domains, adaptive triangulation and approximation of trimmed curved surface patches and other engineering applications using the medial axis transform are also discussed.

scholarly journals Finite element methods for compressible Stokes equations with inflow boundary condition

1997 ◽  
Vol 56 (2) ◽  
pp. 217-225
Author(s):  
Jae Ryong Kweon
Keyword(s):  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Error Analysis ◽  
Finite Element Methods ◽  
Stokes Equations ◽  
Discrete Problem ◽  
Unique Existence ◽  
Inflow Boundary Condition ◽  
The One

A finite element method for solving the compressible viscous Stokes equation with an inflow boundary condition is presented. The unique existence of the solution of the discrete problem is established, and an error analysis is given. It is shown that the error in pressure is dominated by the one in velocity and an error at the inflow portion of the boundary.

Order of Accuracy and Sensitivity to Freestream Conditions of a Modified k-ω Turbulence Model for High-Order Finite Element Methods

2020 ◽  
Author(s):  
Nojan Bagheri-Sadeghi ◽  
Brian T. Helenbrook ◽  
Kenneth D. Visser
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Flat Plate ◽  
Turbulence Model ◽  
Finite Element Methods ◽  
Incompressible Flows ◽  
Grid Point ◽  
High Order ◽  
Surface Boundary ◽  
Wall Distance

Abstract Using turbulence models with finite element methods (FEM) can be challenging as the turbulence variables can assume negative non-physical values and hinder solution convergence. A modified k–ω model was recently proposed by Stefanski et al. (2018) to be used with finite element solvers of compressible flows. The model overcomes this issue by replacing k and ω with working variables that ensure positivity and smoothness of k and ω. In this work the applicability of this model for high-order FEM simulations of incompressible flows was examined. The model was implemented for incompressible flow in an hp-FEM solver using streamline Petrov-Galerkin discretization and was validated and verified using a fully-developed channel flow and a boundary layer flow over a flat plate. Several aspects of the turbulence model behavior were studied. These included the possibilitty of getting orders of accuracy higher than 2, and the model’s sensitivity to freestream values of k and ω. The results suggested that higher orders of accuracy are possible when quadratic and quartic basis functions are used. However, this depended on the way the boundary condition for ω was defined. The commonly used boundary condition for ω, which depends on the wall-distance of the first grid point resulted in poor orders of accuracy compared to the so-called slightly-rough-surface boundary condition which is independent of the wall distance of the first grid point. Additionally, results indicated that increasing the nondimensional wall distance of the first gridpoint makes it more sensitive to the value of ω on the wall. Adding a cross-diffusion term to the transport equation for ω is known to significantly improve the accuracy of turbulence model prediction for certain flows and reduce the sensitivity of the original k–ω model to freestream values of turbulence variables. Following a more recent version of k–ω model, this term was added to the turbulence model and some other modifications including a different production term with a stress-limiter were applied. The drag coefficient of the flat plate from the new turbulence model showed similar sensitivity to the freestream values of turbulence variables as the model of Stefanski et al. (2018).

Three-Dimensional Stokes Flow Solution Using Combined Boundary Element and Finite Element Methods

1999 ◽  
Vol 15 (4) ◽  
pp. 169-176 ◽  
Author(s):  
D.L. Young ◽  
Y.H. Liu ◽  
T.I. Eldho
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Finite Element Methods ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Slow Motion ◽  
Diffusion Type ◽  
Fem Model ◽  
Poisson Equations ◽  
Vorticity Equations

AbstractThis paper describes a model using boundary element and finite element methods for the solution of three-dimensional incompressible viscous flows in slow motion, using velocity-vorticity variables. The method involves the solution of diffusion-advection type vorticity equations for vorticity whose solenoidal vorticity components are obtained by solving a Poisson equation involving the velocity and vorticity components. The Poisson equations are solved using boundary elements and the vorticity diffusion type equations are solved using finite elements and both are combined. Here the results of Stokes flow with very low Reynolds number, in a typical cavity flow are presented and compared with other model results. The combined BEM-FEM model has been found to be efficient and satisfactory.

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