Questions tagged [incompressible]
For questions about the modeling of incompressible fluids.
28
questions
2
votes
1
answer
97
views
Why can the weak forms of the Stokes and continuity equations be combined into a single equation?
Consider this Stokes equations,
$$
\left\{
\begin{array}{r}
- \mu \Delta \vec{u} + \nabla P = \vec{f} \\
\nabla \cdot \vec{u} = 0
\end{array}
\right.
$$
Weak form I is:
$$
\...
- 21
1
vote
0
answers
80
views
Fortran - Lid-Driven Cavity Boundary Conditions Error when using SIMPLE method
I am studying Numerical Methods for incompressible flows. part of the tasks is to model the lid driven cavity problem in 2D using the SIMPLE method.
I have been provided with Fortran code that is ...
- 21
0
votes
0
answers
682
views
The mathematical meaning of a zero gradient pressure boundary condition in the Navier-Stokes equations
I would like to solve the Navier-Stokes equations for the unsteady problem of the flow around a circular cylinder. I would like to understand how to write mathematically the boundary condition for the ...
2
votes
0
answers
75
views
How to assign initial velocity field and handle pressure-velocity coupling in FVM?
I am trying to solve the 2D incompressible Navier-Stokes equations for laminar flow over a backward facing step using the finite volume method.
This is the plot that I generated of a generic mesh ...
0
votes
1
answer
80
views
Displacement/Pressure Finite Element formulation for Large Deformations (from Bathe)
On page 563 of Finite Element Procedures by Klaus-Jürgen Bathe the author states that governing equations of the displacement/pressure finite element formulation for large deformations is given as
$$
\...
- 265
1
vote
0
answers
236
views
Lumped mass matrices for higher-order finite elements for CFD
Given that some of the mass lumping techniques, for example, row-sum lumping does not produce practically viable lumped mass matrices for all the element shapes, what are the techniques used for mass ...
- 934
1
vote
0
answers
100
views
Stokes problem with imposed acceleration on boundaries (projection scheme)
I am trying to solve FSI problems with finite elements and using a projection scheme (I am taking as reference the review of Guermond:
Guermond, J. L.; Minev, P.; Shen, Jie, An overview of ...
- 11
4
votes
1
answer
113
views
How to deal with pseudo-compressibility of lattice Boltzmann method when you are calculating mass flux?
In lattice Boltzmann method, we have a concept, which is called pseudo-compressibility and it is defined based on the fact that LBM simulates incompressible flows by having small Mach number to ensure ...
- 2,332
2
votes
0
answers
47
views
Verification on pressure predictor method for CFD code
I have developed a python code for a lid-drive cavity model. However, my results are not converging. The algorithm of my code looks like this:
Euler Momentum Equation looks like this:
$$\frac{u^{n+1}...
- 123
0
votes
2
answers
190
views
Taylor-Hood finite hexahedral elements, pressure diverging
I am developing a FEM fluid solver using the Taylor-Hood algorithm, i.e. quadratic interpolation for velocity, and linear for pressure.
I have developed the code for 2-D quadrilaterals and triangles, ...
4
votes
3
answers
935
views
How can I make sure the flow is divergence-free when I use moving mesh?
I am using projection method and P2/P1 finite element method to solve the incompressible Navier-Stokes equations while the mesh is constantly adapted as the body moves (edge swapping, splitting and ...
3
votes
1
answer
457
views
Can we simulate incompressible flows using the (slight) density changes to give pressure?
A common approach says an incompressible flow has velocity divergence of 0; use this to solve for pressure in the Navier Stokes momentum equation. Or, using the Helmholtz Decomposition "project" the ...
- 364
2
votes
4
answers
1k
views
Simple methods for solving 2D steady incompressible flow?
I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 ...
- 21
1
vote
0
answers
147
views
Diverged HDG solution for 2D incompressible Navier-Stokes test case at SMALL time step. Why?
I wrote a hybridizable Discontinuous Galerkin code for transient Navier-Stokes flow,
with thanks to Martin Kronbichler and Scott Miller's step-51 code in Deal.II. The main algorithm
is from Nguyen ...
- 31
1
vote
1
answer
96
views
cavity flow with only an external force. Why does it circulate?
Using the code from http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf, I simulated cavity flow with an external force with the boundary conditions on the all 4 sides are $u=v=0$ and $\frac{\...
- 203
2
votes
1
answer
209
views
Adding an external force to Chorin's projection method for the Navier-Stokes equation
I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf
I want to solve an optimization problem using this Navier-Stokes code as constraining PDE. Now I am trying to add ...
- 203
1
vote
2
answers
2k
views
Boundary condition for Pressure in Navier-Stokes equation
I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf
I could not really understand the description. Could someone explain a little bit more?
It says,
"For the lid ...
- 203
1
vote
1
answer
356
views
The pressure correction equation in Chorin's Projection Method for the Navier-Stokes equation
I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf
It says applying the divergence to both sides of this equation
$$\frac{1}{\Delta t} U^{n+1} - \frac{1}{\Delta t} U^{...
- 203
3
votes
2
answers
360
views
Does artifical dissipation term makes scheme inconsistent?
Central schemes like JST uses artificial dissipation for the stabilization. This modification is an artificial one. Does this additional term makes system inconsistent? Can we expect this term to be ...
- 489
5
votes
2
answers
1k
views
Incompressible Navier-Stokes equations: Is projection method exact?
Is the projection method of integrating Navier-Stokes equations exact?
Take the incompressible flow equations:
$$
\frac{\partial\mathbf{u}}{\partial t} = -\mathbf{u}\cdot \nabla \mathbf{u} -\nabla ...
- 452
2
votes
0
answers
349
views
Treatment of Neumann (Traction) boundary conditions using projection methods
I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity:
$\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$
...
- 21
6
votes
2
answers
2k
views
Finite elements for Stokes with traction boundary conditions
Suppose we are given the Stokes equations with Neumann conditions on part of the boundary:
$-\nabla\cdot\boldsymbol{\sigma} = \mathbf{f}, \quad \text{and} \quad \nabla\cdot \mathbf{u} = 0 \quad \...
- 1,074
3
votes
3
answers
160
views
Test case suggestion for incompressible flow with ALE method on deforming grids
I'm working on a finite-volume discretization method with implicit time-integration for the incompressible Navier-Stokes equations in Arbitrary Lagrangian-Eularian (ALE) form. So far I've tested the ...
- 1,055
7
votes
3
answers
235
views
Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?
In Theorem 6.2 of their 2003 paper on "Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal., 40(6), 2171–2194", D. Schötzau, Ch. Schwab, and A. Toselli prove a bound of the $\inf$-$\sup$ ...
- 1,124
16
votes
1
answer
6k
views
Pressure as a Lagrange Multiplier
In the incompressible Navier-Stokes equations,
\begin{align*}
\rho\left(\mathbf{u}_t + (\mathbf{u} \cdot \nabla)\mathbf{u}\right) &= - \nabla p + \mu\Delta\mathbf{u} + \mathbf{f}\\
\nabla\cdot\...
- 1,493
4
votes
2
answers
2k
views
Fractional-step method
I am about to start my journey into the world of CFD and wanted to start with the Fractional-step method for solving the incompressible Navier-Stokes equations. Could you perhaps suggest some articles ...
- 425
10
votes
3
answers
2k
views
manufactured solutions for incompressible Navier-Stokes -- how to find divergence-free velocity fields?
In the method of manufactured solutions (MMS) one postulates an exact solution, substitutes it in the equations and calculates the corresponding source term. The solution is then used for code ...
- 1,055
14
votes
1
answer
460
views
What spatial discretizations work for incompressible flow with anisotropic boundary meshes?
High Reynolds number flows produce very thin boundary layers. If wall resolution is used in Large Eddy Simulation, the aspect ratio may be on the order of $10^6$. Many methods become unstable in this ...
- 25.7k