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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,...

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69 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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26 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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39 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
57 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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64 views

Is it possible to solve the incompressible Navier-Stokes equations by solving just one matrix per timestep?

I'm trying to simulate the 2D incompressible Navier-Stokes equations using a finite difference scheme that uses the implicit Backwards Euler method for moving the simulation forward in time. I have ...
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60 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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82 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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54 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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69 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
83 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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83 views

Local/Explicit Time Stepping for Incompressible Viscous Flow

I've been writing a Finite-Volume based solver for fun and have been looking at getting it to run in parallel. While searching for methods I ran across the local time-stepping methods for the Euler ...
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1answer
115 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
378 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
237 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
217 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
285 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
207 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
265 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 ...
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1answer
249 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 ...
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1answer
82 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
138 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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1answer
441 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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204 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
85 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
184 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
67 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
103 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
96 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
366 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
151 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
681 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
193 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^{...
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3answers
314 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 \...
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1answer
857 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 ...
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1answer
140 views

Relaxation Parameters for Steady Navier-Stokes

I am working on a project involving steady solutions for the Navier-Stokes Equations. In the past I've only worked with the unsteady Navier-Stokes, so some of this is new to me. In particular, at ...
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0answers
73 views

Oscillations in Chorin's method due to the BC

I am pretty new to the CFD and I wanted to start with Chorin's projection. The starting problem is just a free jet flowing in the investigated area. I got terrible oscillations almost immediately and ...
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1answer
510 views

Pressure boundary condition in Navier-Stokes equations

I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with ...
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0answers
35 views

BC's for intermediate velocities in Implicit Fractional Step Methods

Lately, I was reading some seminal papers on Fractional Step Algorithms and I found this one: Kim, D., Choi, H. A Second-Order Time-Accurate Finite Volume Method for Unsteady Incompressible Flow on ...
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0answers
50 views

Finite differences for incompressible viscous fluid equations

I am working with the equations for incompressible viscous fluid: $$ \partial_t \vec{\omega} + (\vec{u}\cdot\nabla)\vec{\omega} = \nu\nabla^2\vec{\omega} $$ $$ \nabla^2 \vec{\psi} = -\vec{\omega} $$ $...
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1answer
538 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 ...
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2answers
973 views

Recovering pressure from velocity or streamfunction fields

I am interested in 2D channel flow of an incompressible Stokes fluid (Re << 1), with periodic boundary conditions in the x-direction and no-slip at the walls in the y-direction. I have existing ...
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2answers
116 views

Stokes Equation in “two-fold saddle point” form?

Are there papers that deal with the (nondimensionalized) Stokes equation for incompressible fluid flow in a "doubly mixed" form like the following? \begin{align*} 0&=\underline{\epsilon} + \frac{...
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1answer
339 views

How to define residual in multigrid approach?

I wish to solve the two-dimensional Navier Stokes equations using multigrid method on a collocated grid using the Predictor-Corrector method mentioned below. But first, let me elaborate on what I had ...
4
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1answer
121 views

Decaying turbulence and simulation

I am a beginner in CFD having written few codes for laminar flow cases using SIMPLE and some other explicit solvers. Now, I want to use my solvers and some other models to solve for the turbulent flow ...
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1answer
163 views

Is this finite difference approach correct?

I am solving incompressible 2D Navier-Stokes equations with zero y-component velocity. The geometry is a simple 2D pipe of a length $L$ and diameter $W$ and there is only two boundary conditions: Non-...
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1answer
230 views

Outflow boundary condition

I know that in outflow boundary we assume a zero normal gradient condition and use upwind scheme for approximation. However, I saw this sentence in a book which I do not understand; "Convective fluxes ...
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1answer
107 views

In which cases an interface tracking/capturing method needed along with Navier-Stokes solver for flow?

In my view, it is needed, To save computational time. To define accurate boundary conditions at interface where properties changes drastically. To solver 2 phase problems as single phase only. To ...
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2answers
344 views

Lid-driven Cavity benchmark in 3D. Classical paper to compare

I'm looking for a benchmark for the lid-driven cavity problem in 3D to compare the results of my code. In 2D I used: U. K. N. G. Ghia, K. N. Ghia and C. T. Shin (1982) High-Re solutions for ...
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1answer
190 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, ...
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0answers
271 views

Periodic boundary conditions for solving Navier Stokes Equations on a Staggered Grid

I want to solve two dimensional Navier Stokes equations on a staggered grid for the case of Taylor-Green Vortex. My initial conditions are standard sine and cosine functions. As I am aware, I should ...