# A Hermite finite element method for incompressible fluid flow

@article{Holdeman2010AHF, title={A Hermite finite element method for incompressible fluid flow}, author={Jonas T. Holdeman}, journal={International Journal for Numerical Methods in Fluids}, year={2010}, volume={64} }

We describe some Hermite stream function and velocity finite elements and a divergence‐free finite element method for the computation of incompressible flow. Divergence‐free velocity bases defined on (but not limited to) rectangles are presented, which produce pointwise divergence‐free flow fields (∇·uh≡0). The discrete velocity satisfies a flow equation that does not involve pressure. The pressure can be recovered as a function of the velocity if needed. The method is formulated in primitive…

## 15 Citations

### Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis

- Computer ScienceJ. Sci. Comput.
- 2015

The dynamical mechanism of the boundary layer separation for a triangular cavity flow with Reynolds numbers, including the precise values of bifurcation location and critical time, are reported in this paper.

### A Combination of a Special Hermite Finite Element with Collocation for a Reaction-Diffusion Type Equation

- MathematicsLobachevskii Journal of Mathematics
- 2019

In the paper, we propose an efficient method based on the use of a bicubic Hermite finite element coupled with collocation for the reaction-diffusion equation with a variable coefficient. This…

### Hierarchical p‐version C1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates

- Computer ScienceInternational Journal for Numerical Methods in Engineering
- 2019

Numerical results demonstrated that p‐version finite elements that have curve boundaries for C1 problems are computationally inexpensive and converge fast for problems with regular and irregular domains.

### Numerical approach of free and forced elastic vibrations using high-regularity Hermitian partition of unities

- Engineering
- 2020

In this paper, shape functions with regularity up to $$C^{2}$$ C 2 were developed for the four-node quadrilateral finite element considering the partition of unity property. This high-regularity…

### C1 conforming quadrilateral finite elements with complete second-order derivatives on vertices and its application to Kirchhoff plates

- Mathematics
- 2020

The classical problem of the construction of C1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method. In…

### Method for Modelling of Circulation of Lubricating Fluid in Models of Machine-Building Products

- Engineering
- 2019

A method for the computation of the lubricating fluid circulation is presented. It uses orthogonal meshes of the inner volume of assemblies and a particle-in-cell method to calculate the flows of…

### Modelling and simulation of flow induced vibrations in vertical axis wind turbine blade

- Engineering2017 14th International Bhurban Conference on Applied Sciences and Technology (IBCAST)
- 2017

The interaction between fluids and structures play an important role in number of fields. Important applications can be found in wind turbine blades, airplane wings, tall buildings, suspension…

### Simulation of droplet ejection based on electromechanical parameters & chemical condition for controlling inkjet printing devices

- Materials Science, Engineering
- 2020

In this study, the droplets in inkjet printing have been simulated based on mechanical parameters including temperature and pressure changing and also the chemical condition contain dielectric of…

## References

SHOWING 1-10 OF 26 REFERENCES

### A test problem for outflow boundary conditions—flow over a backward-facing step

- Physics
- 1990

A numerical solution for steady incompressible flow over a two-dimensional backward-facing step is developed using a Galerkin-based finite element method. The Reynolds number for the simulations is…

### Introduction to Theoretical and Computational Fluid Dynamics

- Physics
- 1996

Preface Note to the Instructor Note to the Reader 1 Kinematic structure of a flow 2 Kinematic analysis of a flow 3 Stresses, the equation of motion, and vorticity transport 4 Hydrostatics 5 Exact…

### On a Galerkin--Lagrange Multiplier Method for the Stationary Navier--Stokes Equations

- Mathematics
- 1982

A Galerkin–Lagrange multiplier formulation is used for the numerical solution of the stationary Navier–Stokes equations, in order to avoid the construction of zero-divergence elements. The…

### High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method

- Computer Science
- 1982

### A short note on the reattachment length for BFS problem

- Environmental Science
- 2006

The standard backward-facing step flow problem is solved for steady state laminar case using stream function-vorticity method. The steady state results are obtained as the asymptotic solution of the…

### The no Boundary Condition Outflow Boundary Condition

- Mathematics
- 1997

We use a one-dimensional model problem of advection– diffusion to investigate the treatment recently advocated by Papanastasiou and colleagues to deal with boundary conditions at artificial outflow…

### Résumé and remarks on the open boundary condition minisymposium

- Computer Science
- 1994

The two minisymposia on OBCs that are summarized in this paper had the objective of finding the best OBC's for a small subset of two-dimensional test problems, but the contributions obtained probably raised many more questions/issues than were resolved.

### BASIS FOR DERIVATION OF MATRICES FOR THE DIRECT STIFFNESS METHOD

- Mathematics
- 1963

Previous developments in the direct stiffness method are reviewed. The advantages of extending the definitions to make the method a variational approach are cited. The finite element formulation of…