Questions tagged [navier-stokes]

Questions about solution methods of the Navier-Stokes equations, related physical constants and non-dimensional number. Also special methods to solve the equations including the assumptions and their implementation in order to simplify them. Also, questions regarding modelling of the non-linear term, coefficients of these model can be subjective of this title.

Filter by
Sorted by
Tagged with
10
votes
3answers
1k 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 ...
3
votes
2answers
347 views

Looking for reference on Streamline Upwind Petrov Galerkin finite elements for incompressible unsteady Navier-Stokes

I am looking for a relatively simple book/paper that explains the basic Streamline Upwind Petrov Galerkin (SUPG) method for solving the incompressible unsteady Navier-Stokes equations. Most of the ...
0
votes
1answer
923 views

How to calculate divergence and vorticity from a velocity field using finite elements

I am in the process of writing a finite element solver for the Navier-Stokes equations and am having trouble computing things like the divergence and vorticity correctly. Currently to compute the ...
3
votes
1answer
772 views

Pressure projection method boundary conditions

When using the pressure projection method to solve the incompressible Navier-Stokes equations do we apply Neumann boundary conditions for pressure only where there are associated no-slip velocity ...
1
vote
1answer
158 views

How to update velocity to include pressure when using P2/P1 elements

I am in the process of writing a finite element code to solve the Navier-Stokes equations using the theta method for time stepping (basically Crank-Nicholson for diffusion and forward Euler for ...
3
votes
1answer
757 views

2D Poisson Solver for Taylor Green Vortex Problem

I am trying to write a 2D Navier Stokes solver using an RK3 for time advancement in python. For debugging, I have converted the RK3 to an Euler step for simplicity. Checking my divergence for my ...
3
votes
1answer
267 views

precision loss in non-trigonometric, periodic functions using FFTW and NaNs after marching forward in time (Fortran)

I have developed a pseudospectral solver of the Navier-Stokes equations using FFTW. I tested my formulation of right hand sides (RHS) of the NS equations against standard trigonometric functions (...
1
vote
0answers
64 views

Help about Fluid-Fluid coupling techniques

I need a little help and advice with a project I want to do: the idea is to "couple" (I don't know whether I can call it like this) a conservative Navier-Stokes Solver (Fractional-step, 2nd order FDM) ...
1
vote
0answers
185 views

Visualization of solution for a MAC grid

So I implemented the projection method as in Chorin (1969) for the solution of the Navier-Stokes Equations with the Boussinesq Approximation, using a 2nd Order accurate FD scheme. The primitive ...
2
votes
0answers
134 views

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
2
votes
0answers
356 views

Stationary 2D/3D Navier-Stokes source code

Trying to solve stationary Navier-Stokes problem for incompressible laminar Newtonian fluid. I've found a couple solutions for instationary Navier-Stokes equations (like FeniCS examples or CFD Python)...
3
votes
3answers
940 views

Solving Stokes flow with walls using Oseen tensor

Introduction I've developed a code to solve for generalised, incompressible 2D Stokes flow $\eta \nabla^2 \mathbf{v} - \nabla p + \mathbf{S} = 0$ $\nabla . \mathbf{v} = 0$ where $\mathbf{S}$ can ...
1
vote
2answers
140 views

Nondimensional gas constants

I am doing a nondimensional Navier-Stokes simulation, but it's not exactly clear what values to use for the various gas constants: $R$, $C_v$, and $C_p$. Obviously, once I know one of these and $\...
2
votes
0answers
296 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: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
5
votes
2answers
485 views

Choice of spaces for mixed formulation for Poisson Equation Or Darcy equation

Consider the mixed formulation of the Poisson/Darcy system for a region $\Omega$: $\alpha \mathbf{v} + \nabla p = f \\ \mathrm{div}[\mathbf{v}] = 0 $ with the boundary conditions $\mathbf{v}\cdot ...
6
votes
1answer
7k views

Type of Navier-Stokes equation

What type equation Navier-Stokes is: Elliptic, parabolic, or hyperbolic? Should it give always the same answer no matter what is the initial condition? How these statements could be proved?
2
votes
3answers
1k views

Implementation of Navier-Stokes Equation for Ocean Waves

I am doing an undergraduate research to model ocean waves in shallow waters in real time. I am trying to base my research on Navier-Stokes equations since they produce the most accurate mathematical ...
4
votes
1answer
3k views

Comparison of Lattice Boltzmann Method vs Traditional Navier-Stokes based Methods

I have a choice of two options, analysing and implementing Lattice Boltzmann methods or traditional Navier Stokes based methods. I'm a CFD newbie and I have a rough idea (though not rigorous enough to ...
3
votes
2answers
604 views

Solving Navier Stokes Eq using Gauss–Seidel and Finite Difference [closed]

I am trying to solve the following set of equations using a finite-difference approach and an iterative solver (Gauss-Seidel). Continuity Equation: $\frac{\partial V_x}{\partial x} + \frac{\partial ...
1
vote
0answers
226 views

High-order continuous Galerkin Navier-Stokes solver in deal.II

I looked at the list of publications related to deal.II, but it seems that when it comes to Navier-Stokes equations, everyone speaks about Discontinuous Galerkin solver in their papers. I know there's ...
6
votes
1answer
123 views

L1 functional setting for Navier-Stokes with finite elements

Typical finite element problems assume $L^2$ which is a Hilbert space, but I've heard that $L^1$ for Navier-Stokes results in less overshoots/undershoots, but $L^1$ is not Hilbert. The dual space for $...
2
votes
1answer
458 views

2d pseudo-spectral turbulence simulation with random initial velocities

I am trying to write a 2d pseudo-spectral DNS code with random initial velocities. This is kind of a classic simulation where the very tiny vortices group together forming larger and larger vortices ...
3
votes
2answers
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 ...
7
votes
2answers
1k views

What are some of the differences between using a Lagrangian and Eulerian framework to quantify passive scalar dynamics?

On one hand, one may seed the domain with particles and track their trajectories in the Lagrangian sense by implementing a Lagrangian particle tracking model. On the other hand, one may use the ...
7
votes
2answers
969 views

Feasibility and software for acoustic simulation

I'm looking at doing a finite-element simulation of air flow essentially for the purposes of approximating the response to an external audio impulse of a smallish (~10-30 cm scale), stationary 3D-...
7
votes
5answers
2k views

Open source codes for 2D instationary Navier Stokes equations

What open source tool can be recommended for solving 2D instationary Navier Stokes equations (in simple geometries, but with high Reynolds numbers)? Most packages I found, I'm not very lucky with. ...
5
votes
0answers
188 views

Time-stepping for coupled nonlinear PDEs

What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow), $$ \begin{cases} \rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla \mathbf{u}\...
11
votes
2answers
351 views

What is the underlying structure of scientific code performance?

Consider two computers with different hardware and software configurations. When running the exact same serial Navier-Stokes code on each platform it takes x and y time to execute one iteration for ...
3
votes
3answers
142 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 ...
14
votes
1answer
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\...
6
votes
0answers
99 views

Benchmarks or generic configurations for optimal flow control

I am about to test my algorithms for solving optimal control problems of type: Find an input $u$, such that for a time interval $(0,T]$ the cost functional $$J(v,u) = \mathcal M(v(T)) + \int_0^T\...
4
votes
1answer
109 views

Is stabilization of energy equation needed when momentum equation needs it?

When SUPG/PSPG stabilization is added to momentum equation of flow problem, is needed stabilization for energy equation also? I would guess that when stabilization for velocity works fine so one gets ...
4
votes
2answers
2k views

Software for 3D Navier-Stokes equation

What is the best software for solving and simulating the 3D Navier-Stokes equation for incompressible laminar non-Newtonian fluid flow?

1 2
3