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.
124
questions
1
vote
2answers
416 views
Imposing total pressure over surface in FEM
I am trying to solve Stokes problem using Finite element method.
My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?
4
votes
1answer
128 views
Projection method FVM poisson part, adding source term
The idea of the method is to decompose the Navier-Stokes equation into the solenoidal and irrotational parts.
$$\frac{\partial u}{\partial t}+u(\nabla \cdot u)=-\frac{1}{\rho}\nabla p+\nabla ^2 u$$
...
0
votes
0answers
63 views
Pressure boundary conditions in Stokes Equation in 2D
I am solving the steady-state incompressible Stokes equations in 2D:
\begin{equation}
\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} = 0,
\end{equation}
\begin{equation}
\mu\left[\...
3
votes
2answers
96 views
Efficient schemes for solving the extended Saddle point problem
I am interested in knowing some efficient techniques for solving the following extended Saddle point problem.
\begin{align}
\begin{bmatrix}
A & B^T & C^T \\
B & 0 & 0 \\
C & ...
1
vote
0answers
70 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 ...
2
votes
1answer
65 views
Fix for FD WENO method for multi-component compressible flows
I'm solving two-dimensional four-component compressible Navier-Stokes equations with finite-difference WENO approach. The equations are pretty standard:
$$
\frac{\partial U}{\partial t} +
\frac{\...
1
vote
2answers
135 views
How to apply central difference to viscous fluxes in 2D Navier-Stokes equations?
I'm trying to solve 2D unsteady compressible Navier-Stokes equations with finite-difference or finite-volume method. Here is the system, it's pretty standard:
$$
\frac{\partial U}{\partial t} +
\frac{...
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 ...
3
votes
0answers
61 views
Explicit DG time step restriction for compressible Navier-Stokes equations
Hesthaven's book 1 mentions the following time step restriction for Navier-Stokes equations (see (7.32) in 2008 edition)
$$
\Delta t \approx \frac{h}{N^2} \frac{C}{|u| + |c| + \frac
{N^2 \mu}{h}}
$$
($...
2
votes
2answers
86 views
Different form of the Navier--Stokes equations
Normally I write the incompressible Newtonian isothermal flow Navier--Stokes equations as follows:
$$\displaystyle
\frac{\partial v}{\partial t}
-\nu\Delta v
+\color{red}{(\nabla v)v}
+...
4
votes
4answers
3k views
How to deal with nonlinear term in Navier Stokes equations (finite element code)
I am trying to solve the Navier Stokes equations using the finite element method. I plan on using the pressure correction method to deal with the pressure and an implicit time stepping scheme for ...
2
votes
0answers
51 views
Haw to apply central difference to viscous flux in energy equation?
In many modern papers Navier-Stokes equations are solved with finite-difference or finite-volume methods using WENO reconstruction for non-viscous fluxes and central differences for viscous ones. It ...
2
votes
2answers
123 views
Simplest way to “upgrade” from Euler equations to Navier-Stokes equations in FV or FD framework
I have quite a lot of experience solving unsteady Euler equations, including multi-component ones, with in house-coded finite-difference and finite-volume methods, including MacCormack and MUSCLE ...
2
votes
0answers
51 views
Solving Stokes Equations in 3D - Do I need to treat pressure-velocity coupling iteratively?
I need to develop a code to solve Stokes Equations in 3D in cubic geometries (structured grid, uniform mesh spacing).
My code needs to take a pressure gradient in one direction as a BC (pinlet=p1, ...
3
votes
0answers
65 views
How to construct a Fortin Operator for Crouzeix-Raviart Element?
I want to prove the LBB condition for the Stokes Equations discretised by the Crouzeix-Raviart element.
The continuous Stokes Equation in the weak formulation is
Find $u \in H_0^1(\Omega, \mathbb{R}^...
1
vote
0answers
93 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 ...
0
votes
1answer
88 views
FDM on nonlinear PDEs
I'm working with a 2D Navier Stokes PDE in the unstabilized version - the equation is a linear equation of the type $\frac{∂u}{∂t} = F(u,t)$.
In order to perform time discretization with FDM (finite ...
5
votes
1answer
269 views
What kind of a researcher am I?
So far, I've worked a bit in modeling, simulations and simple lab experiments, and I've really enjoyed all three research methods to approach a single research question. I can write tricky (in terms ...
0
votes
0answers
74 views
Open Boundary Conditions for Solving Navier Stokes in moving ALE domain
I'm trying to solve the problem of a body freely rising in a fluid due to gravity, the density of the body is just slightly less than that of the fluid.
The body is rigid, so I have to solve a ...
0
votes
0answers
29 views
RANS equations in the ALE formulation
I am simulating an incompressible flow of a newtonian fluid over an oscillating plate using OpenFOAM . As far As I know, in this case, OpenFOAM uses the Arbitrary Lagrangian Eulerian formulation. ...
0
votes
0answers
73 views
Numerical flow visualization in 2D for a moving boundary,
I have a rigid body that moves according to a set of governing ODEs, and I'd like to numerically visualize the vortices that are shed by this object. How could I proceed?
I've been reading up on the ...
0
votes
0answers
64 views
The relation between PDE order and discretization order
In Jasak's Ph.D. thesis (2000), a notion is given about discretization of a transport equation:
For good accuracy, it is necessary for the order of the discretization to
be equal to or higher than the ...
0
votes
1answer
130 views
How to visualize the vorticity / flow for a rigid body moving through a fluid?
How can I write down two-dimensional Navier-Stokes equations for a simple rigid object immersed in a flow and freely falling due to gravity? I'm trying to view the vorticity that's induced by the ...
9
votes
2answers
619 views
Time discretization of the variational formulation of the Navier-Stokes equation
I've asked this question on mathoverflow too.
Let
$T>0$
$I:=(0,T]$
$d\in\mathbb N$
$\Lambda\subseteq\mathbb R^d$ be nonempty and open, $$\mathcal V:=\left\{\phi\in C_c^\infty(\Lambda,\mathbb R^d):...
2
votes
1answer
148 views
What is the correct way to calculate deviatoric stress tensor in lattice Boltzmann method?
Due to my previous question, where I asked about flux calculation in lattice Boltzmann (LB) method here, I have more or less same question for deviatoric stress tensor calculation due to pseudo-...
2
votes
2answers
908 views
Lattice Boltzmann methods vs Navier stokes/ other eulerian methods for *water* simulation
Note, there is already a question here, however the answers don't answer the original question, let alone specific considerations when dealing with nearly in-compressible fluids (water). Another ...
1
vote
0answers
23 views
Equi-order in pressure correction schme of Navier-Stokes equation
I am wondering if there is an stabilized equi-order scheme in pressure correction scheme in solving Navier-Stokes equation? Usually P2-P1 element combination is used to solve NS equation, and a PSPG ...
1
vote
0answers
80 views
Governing equations vs Transport equations
This is a basic question. But I did not find any explanations for this. How are governing equations, like mass, momentum, energy conservations equations, different from 'Transport equation'?. Is a ...
2
votes
2answers
184 views
Automatic timestep adjustment in a CFD solver
I have developed my own 3D Finite Volume Navier-Stokes solver based on projection method for nonuniform grid. I am looking to incorporate automatic timestep adjustment at each time step based on ...
0
votes
0answers
55 views
Stokes Equation fails to converge for an ellipse
This might be because of the mesh, but the following code blows up for all values of b not 1. Does anybody have any experience working with the ellipse mesh in Fenics?
...
0
votes
1answer
86 views
Is “Gradient Computation” in Finite Volume Discretization Really 2nd order accurate?
Based on this, pp 245, we go through these steps to discretize a gradient statement, namely $\nabla\phi$:
1- Gauss theorem reads,
$$
\int_V\nabla \phi dV = \oint_{\partial V}\phi dS
$$
2- Integral ...
2
votes
1answer
4k views
PDEs in their weak form in Comsol
If a physical model is not listed in the wizard, we can use Comsol's weak form to enter PDE's (governing equations of a system) in their weak form. How can it be done ?
for example: 2 equations of ...
0
votes
0answers
126 views
Double mach reflection at a inclined wedge
I am running into a strange problem when solving the 2D compressible Euler equations on a inclined wedge. To elaborate, my top boundary condition seems to emitting some type of instability. I have ...
0
votes
0answers
48 views
3D Tollmien-Schlichting Waves Imposed in a Channel Flow (Are Physics correct?, etc)
So I am trying to do some further tests on a 2nd-order code Incompressible Navier Stokes equations, by studying transition to turbulence in a Poiseuille flow. Specifically, I'm interested to see ...
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 ...
0
votes
2answers
142 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, ...
1
vote
0answers
55 views
Combining fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method
I'm thinking to couple my fluid flow solver based on lattice Boltzmann method with a mechanical deformation solver based on finite element method to take account for solid deformation in my models. In ...
1
vote
0answers
317 views
Inflow and outflow boundary conditions for advection-diffusion equation
I'm trying to solve this advection-diffusion equation (ADE):
$$\frac{\partial \phi}{\partial t} + \nabla \cdot (-D \nabla \phi + \mathbf{u} \phi) = 0$$
In fact, this ADE framework is coupled to a ...
4
votes
1answer
336 views
How to go from turbulent RANS to laminar Navier-Stokes and Euler
SU2 is an open-source CFD suite that is built around a RANS-solver. The main PDE that is solved, is the following:
$$
\frac{\partial}{\partial t} \mathbf{U} + \nabla \cdot \mathbf{F^c} - \nabla \cdot ...
2
votes
0answers
116 views
Derive total energy balance equation from Chapman-Enskog analysis of lattice Boltzmann equation
I'm interested to derive the total energy balance from Chapman-Enskog analysis of lattice Boltzmann equation (LBE). I know, I should go to the second moment of LBE (zeroth moment gives mass ...
5
votes
0answers
129 views
How can Navier--Stokes equations have asymmetric solutions such as Karman vortex streets
The Navier--Stokes equations are axially symmetric, so with symmetric boundary conditions, how can features such as Karman vortex streets develop?
I understand that in reality symmetry does never ...
1
vote
1answer
1k views
Simple finite volume method for compressible Navier-Stokes equations
I am interested in writing a simple, cell-centered, 2D FVM code for the unsteady, compressible Navier-Stokes equations (including shocks). Most of my experience is with finite difference and finite ...
6
votes
2answers
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 ...
3
votes
0answers
73 views
Solving numerically a linearized system of elliptic (?) Navier-Stokes equation (Shallow Water Derived)
For my PhD Thesis, my advisor asked me to build a solver inspired from the article "Optimal Control Theory Applied to an Objective Analysis of a Tidal Current Mapping by HF Radar, J-L Devenon, 1989". ...
0
votes
3answers
374 views
Turbulence Pseudospectral Code
I am writing a 2D pseudo spectral code for turbulence in a box with 1024 grid points with 3/2 aliasing scheme in the vorticity/stream function formulation. the vortices tends to appear very slowly and ...
3
votes
0answers
153 views
Non-reflecting boundary conditions for compressible Navier-Stokes equations
I have some questions about the implementation of non-reflecting OUTFLOW boundary condition for Navier Stokes equations.
Following
Poinsot, Lele "Boundary Conditions for Direct Simulations of ...
1
vote
1answer
120 views
Simulating Stokes flow with an obstacle
I was asked to compute the Stokes flow (i.e. a low Reynolds fluid) near and obstacle. This is the first time I face a fluid and I am lost. What reference/general ideas/big theorems can you recommend ...
6
votes
3answers
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 ...
2
votes
1answer
240 views
Galerkin method for a system of nonlinear PDEs
Suppose I have a nonlinear system of PDEs. I am actually interested in Navier-Stokes, but, for the sake of simplicity and example, suppose I had
$$
\frac{\partial f}{\partial t} - f \frac{\partial g}{...
2
votes
1answer
1k views
CFL condition in Stokes equation
Does the CFL condition play any role in a pure Stokes flow, i.e. convective term is neglibile, or vanishing? If not, what is the "equivalent" condition for stability? I have read something about the ...
