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.

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14
votes
1answer
17k views

How to formulate lumped mass matrix in FEM

When solving time dependent PDE's using the finite element method, for example say the heat equation, if we use explicit time stepping then we have to solve a linear system because of the mass matrix. ...
4
votes
1answer
2k 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 ...
7
votes
2answers
4k views

FEniCS: separate boundary conditions in normal and tangential direction of mesh boundary

Given a vector-valued PDE, I'd like to enforce the boundary conditions $$ \vec{n}\cdot u = g\\ \vec{n}\cdot \nabla (\vec{t}\cdot u) = 0 $$ on the solution $\vec{u}$. If the boundary happens to align ...
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 ...
16
votes
1answer
244 views

Usefulness of elements with mesh-dependent stability

After doing some mathematics related to the stability of elements in 3D Stokes problem I was slightly shocked to realize that $P_2-P_1$ is not stable for an arbitrary tetrahedral mesh. More precisely, ...
7
votes
3answers
524 views

Mixed Finite Element Method for the Stokes System—Some Implementation Details

I am currently working on my bachelor’s diploma. The research concerns mixed finite element method for the 2D Stokes system $$ - \Delta \boldsymbol u + \nabla p = \boldsymbol f, \quad \boldsymbol x \...
1
vote
2answers
1k views

New to CFD, Lattice Boltzmann or Navier-Stokes?

I apologize if some of my questions are naive; I am very new to computer simulations and fluid-dynamics. I am going to start a PhD in early 2017, and I would like to bone-up on some Computational ...
11
votes
2answers
347 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
906 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 ...
6
votes
2answers
439 views

Implementing the pressure correction method using finite elements

Ok so I am nearing the completion of my finite element Navier-Stokes solver that uses the $\theta$-method for time stepping and the pressure correction method for the pressure. I am following the ...
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 (...