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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41 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, ...
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49 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}^...
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90 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 ...
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1answer
59 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 ...
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63 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 ...
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1answer
248 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 ...
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20 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. ...
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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 ...
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53 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 ...
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1answer
125 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 ...
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39 views

Pressure boundary conditions in Stokes Equation in 2D (Finite Volumes)

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[\...
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1answer
85 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-...
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338 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 ...
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22 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 ...
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55 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 ...
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50 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? ...
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2answers
160 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 ...
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1answer
77 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 ...
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112 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 ...
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38 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 ...
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2answers
129 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, ...
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45 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 ...
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220 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 ...
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1answer
204 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 ...
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107 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 ...
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110 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 ...
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68 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". ...
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136 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 ...
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1answer
116 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 ...
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1answer
201 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}{...
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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 ...
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2answers
363 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?
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1answer
555 views

How to implement finite difference method for one dimensional Navier-Stokes PDEs

I am trying to use backwards finite difference method to numerically solve a pair of partial differential equations: $\frac{\partial \left(pv\right)}{\partial x}+\frac{\partial p}{\partial t}=0$ $\...
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3answers
352 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 ...
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0answers
228 views

Physics of explosions: just vorticity?

eg 1 2. Is it just vorticity? What's actually happening? (Similar: steam engines, volcanoes, clouds). examples are grid-based, using "vorticity confinement" in Phoenix FD. EDIT Some techniques: "...
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2answers
303 views

Can we simulate compressible flows by simple direct explicit calculation, without solving systems of linear equations (such as Poisson eq)?

Is this is plausible at all? It seems the most obvious/naive approach, so there's probably good reasons why it's not used - what are they? Viscosity is not important. Starting with inviscid Navier ...
3
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1answer
319 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 ...
2
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1answer
88 views

Deposition model in laminar flow

I have a chamber full with a fluid flowing horizontally in laminar regime from one side to the other. It carries a suspension with concentration $c$. This suspension also falls to the bottom of the ...
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0answers
189 views

Rhie--Chow interpolation on PDE level

The Rhie--Chow [1] interpolation seems to be a standard tool in the Finite-Volume discretization of incompressible flows. It is commonly defined on the discrete level [2]. In the lecture notes [3] --...
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2answers
597 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):...
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387 views

Rhie and Chow Pressure Velocity Coupling

In a collocated grid, which velocity is used in the convective term in the momentum equation? Is the Rhie and Chow constructed face velocity or an average of the adjacent cell center values(in a ...
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0answers
104 views

Finite difference method for coupled PDEs: optimizing performance (time step, iterations per step)

I'm solving coupled PDEs using finite difference method: Incompressible Navier-Stokes and the divergence-free induction equation (Maxwell's equations) with non-uniform electrical conductivity. The ...
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3answers
212 views

What is the difference between the curl component, and the divergence-free component, of a vector field?

The term divergence-free sounds more general and appears particularly in wavelet-related approaches to the Navier-Stokes equations. However I have yet to find a discussion focusing on the distinction, ...
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1answer
73 views

cavity flow with only an external force. Why does it circulate?

Using the code from http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf, I simulated cavity flow with an external force with the boundary conditions on the all 4 sides are $u=v=0$ and $\frac{\...
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1answer
124 views

Adding an external force to Chorin's projection method for the Navier-Stokes equation

I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf I want to solve an optimization problem using this Navier-Stokes code as constraining PDE. Now I am trying to add ...
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0answers
117 views

Porting from MPI to GPU

Assuming that the underlying algorithm can be ported to multi GPU, what aspects should one consider while porting from MPI (on multiple nodes) to multi GPU (again on multiple nodes)? Making use of ...
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1answer
598 views

Interpolation of velocities on staggered grid (in PIC)

Edit: (copying from my comment) Let's consider the inverse problem when I need to transfer velocities from particles to the grid (inverse bilinear interpolation). How'd I transfer a particle's x-...
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1answer
331 views

Upwind difference for velocity in staggered grid

I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf In the paper, the nonlinear term is treated as mix of central central difference and upwind difference using a ...
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2answers
1k views

Boundary condition for Pressure in Navier-Stokes equation

I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf I could not really understand the description. Could someone explain a little bit more? It says, "For the lid ...
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1answer
238 views

The pressure correction equation in Chorin's Projection Method for the Navier-Stokes equation

I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf It says applying the divergence to both sides of this equation $$\frac{1}{\Delta t} U^{n+1} - \frac{1}{\Delta t} U^{...