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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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, ...
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. ...
4k 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\...
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 ...
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 ...
619 views

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 ...
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 ...
956 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-...
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?
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438 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 ...
778 views

Fluid-structure interaction solver for cardiovascular applications

I would like to start running FSI simulations for cardiovascular applications. More precisely, I'm interested in the behaviour of aortic valve under physiological flow conditions in which the ...
98 views