Skip to main content
6 votes
Accepted

Boundary condition for Pressure in Navier-Stokes equation

When we say that the pressure is only defined "up to a constant", what we mean is this: If $u,p$ is a solution to the Navier-Stokes equations, then $u,p+c$ for any constant $c$ is also a solution. In ...
Wolfgang Bangerth's user avatar
5 votes

Why can the weak forms of the Stokes and continuity equations be combined into a single equation?

To get from weak form I to II, just add the two equations of weak form I. To see the other direction, note that weak form II has to hold for all test functions $\phi$ and $\psi$. That is, you can test ...
cos_theta's user avatar
  • 451
5 votes

Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?

The problem was solved recently: Lederer/Schöberl: Polynomial robust stability analysis for H(div)-conforming finite elements for the Stokes equations
Guido Kanschat's user avatar
4 votes

Incompressible Navier-Stokes equations: Is projection method exact?

Note: I originally posted an answer that I was not 100% pleased with, so I have revised it heavily. 1/20/2017 The projection method is not in an exact approximation to the full system in general. ...
A.Vigs's user avatar
  • 71
4 votes

How can I make sure the flow is divergence-free when I use moving mesh?

It's important to realize that the original velocity field $\mathbf v_0$ is also not divergence free in a pointwise sense. Rather, it is only divergence free when tested with the pressure test ...
Wolfgang Bangerth's user avatar
3 votes
Accepted

Can we simulate incompressible flows using the (slight) density changes to give pressure?

Water (and other fluids that are considered incompressible) are of course in reality compressible -- just not very much, at the pressures and speeds involved in the flow we are modeling. Within the ...
Wolfgang Bangerth's user avatar
3 votes
Accepted

Applicability of 1/7 power law for turbulent flow

Denote $\hat{u} = \frac{u}{u_{max}}$, and $\hat{z} = \frac{z}{z_{max}}$ then your power law is given by $$ \hat{u} = \left(1 - \hat{z}\right)^\frac{1}{n}.$$ Taking the derivative with respect to $\hat{...
Joscha Fregin's user avatar
2 votes

Taylor-Hood finite hexahedral elements, pressure diverging

It's of course hard to tell without knowing the code, the testcase, and your results. So I can't really help you out here. But it is worth pointing out that you are making yourself too much work. Any ...
Wolfgang Bangerth's user avatar
2 votes
Accepted

Adding an external force to Chorin's projection method for the Navier-Stokes equation

I would not bother too much. Chorin's method is known to be a consistent scheme, which means, that for smaller time-steps it will approximate the actual solution. Checkout Gresho's/Sani's book ...
Jan's user avatar
  • 3,418
2 votes
Accepted

The pressure correction equation in Chorin's Projection Method for the Navier-Stokes equation

It is a consequence of the continuity condition ($\nabla \cdot u = 0$), condition (3) at page 2. At chapter 4 at the beginning there is the assumption about the condition (3) is valid. You are at the ...
Mauro Vanzetto's user avatar
2 votes

Simple methods for solving 2D steady incompressible flow?

I cannot comment, so as an answer may I recommend looking at something like: http://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/ form start to finish? This takes the reader from basic ...
DrHansGruber's user avatar
1 vote

Displacement/Pressure Finite Element formulation for Large Deformations (from Bathe)

We have recently proposed a mixed u-p formulation that results in a global symmetric matrix irrespective of the volumetric energy function (for hyperelasticity). The paper contains sufficient details ...
Chenna K's user avatar
  • 944
1 vote
Accepted

How to deal with pseudo-compressibility of lattice Boltzmann method when you are calculating mass flux?

I think that both can be considered to be equally valid. In fact, asymptotically (with an infinite number of lattice) you will tend towards the incompressible athermal Navier-Stokes equations. In this ...
BlaB's user avatar
  • 1,157
1 vote

Taylor-Hood finite hexahedral elements, pressure diverging

I resolved my problem. I added a small pressure coefficient in the continuity equation, let's say $10^{-10}$. In the weak form, this quantity is multiplied by the integral {$N^T$ $N$} (or mass matrix),...
James A Smith's user avatar
1 vote

How can I make sure the flow is divergence-free when I use moving mesh?

What sort of field is it? You've said "divergence free", but do you mean harmonic (zero divergence and curl), solenoidal (non-curl), or a mix of both? The distinction is important because it will ...
Sean Lake's user avatar
  • 143
1 vote

Simple methods for solving 2D steady incompressible flow?

Ironically, there is an iterative method called "SIMPLE" (semi-implicit method for pressure-linked equations) designed to resolve the steady state navier-stokes equations based on a predictor-...
Paul's user avatar
  • 12k
1 vote

Simple methods for solving 2D steady incompressible flow?

With the continuity eqn only, you are missing all the mechanical balance: viscous and/or inertial effects will decide of the streamlines of such a flow. If your major aim is to keep it as simple as ...
Joce's user avatar
  • 362
1 vote
Accepted

cavity flow with only an external force. Why does it circulate?

@Wolfgang Bangerth has a very important point about what $f$ is. The constant external force will not affect your solution unless your BCs allow for motion. In your case, they do not. An easy ...
Charles's user avatar
  • 619
1 vote

Boundary condition for Pressure in Navier-Stokes equation

For the lid driven cavity problem, we apply the Dirichlet boundary condition (or, no-slip boundary condition) to the velocity field $\tt U$, that is, $\tt U = U_{\tt Lid}$ on the moving Lid and $\tt U=...
tqviet's user avatar
  • 151
1 vote
Accepted

Finite elements for Stokes with traction boundary conditions

In the meantime we did some more research into this issue and documented our findings in: M. Huber, U. Rüde, C. Waluga, B. Wohlmuth. Highly sparse surface couplings for subdomain-wise isoviscous ...
Christian Waluga's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible