# Questions tagged [incompressible]

For questions about the modeling of incompressible fluids.

26 questions
Filter by
Sorted by
Tagged with
70 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 ...
1 vote
56 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 ...
69 views

• 123
155 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, ...
788 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 ...
421 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
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
146 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 ...
1 vote
79 views

• 1,054
146 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
227 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 $\inf$-$\sup$ ...
• 1,104
5k 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\...
• 1,443
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
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
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 ...