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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6
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98 views

Benchmarks or generic configurations for optimal flow control

I am about to test my algorithms for solving optimal control problems of type: Find an input $u$, such that for a time interval $(0,T]$ the cost functional $$J(v,u) = \mathcal M(v(T)) + \int_0^T\...
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124 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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187 views

Time-stepping for coupled nonlinear PDEs

What are good references for time-stepping of the coupled incompressible Navier-Stokes-heat equation (Boussinesq flow), $$ \begin{cases} \rho\left(\dot{\mathbf{u}} + \mathbf{u}\cdot\nabla \mathbf{u}\...
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209 views

Reflecting boundary condition posed as a Riemann problem

I am trying to implement a solver for the Euler/Navier Stokes equations. I have a problem implementing boundary conditions for the wall. I am using an unstructured solver. A lot of literature says ...
3
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0answers
58 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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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". ...
3
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148 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 ...
3
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0answers
196 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] --...
3
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114 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 ...
3
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133 views

Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
2
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56 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) $$ \Delta t \approx \frac{h}{N^2} \frac{C}{|u| + |c| + \frac {N^2 \mu}{h}} $$ ($...
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50 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 ...
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50 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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115 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 ...
2
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345 views

Stationary 2D/3D Navier-Stokes source code

Trying to solve stationary Navier-Stokes problem for incompressible laminar Newtonian fluid. I've found a couple solutions for instationary Navier-Stokes equations (like FeniCS examples or CFD Python)...
2
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279 views

Treatment of Neumann (Traction) boundary conditions using projection methods

I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
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92 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 ...
1
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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 ...
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77 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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52 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
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0answers
294 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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2answers
396 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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0answers
232 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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419 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
121 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 ...
1
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0answers
84 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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0answers
36 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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418 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 ...
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0answers
64 views

Help about Fluid-Fluid coupling techniques

I need a little help and advice with a project I want to do: the idea is to "couple" (I don't know whether I can call it like this) a conservative Navier-Stokes Solver (Fractional-step, 2nd order FDM) ...
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0answers
181 views

Visualization of solution for a MAC grid

So I implemented the projection method as in Chorin (1969) for the solution of the Navier-Stokes Equations with the Boussinesq Approximation, using a 2nd Order accurate FD scheme. The primitive ...
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0answers
221 views

High-order continuous Galerkin Navier-Stokes solver in deal.II

I looked at the list of publications related to deal.II, but it seems that when it comes to Navier-Stokes equations, everyone speaks about Discontinuous Galerkin solver in their papers. I know there's ...
0
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73 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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0answers
26 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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63 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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48 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[\...
0
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0answers
54 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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0answers
125 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
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0answers
47 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 ...
0
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0answers
63 views

Finite differences for incompressible viscous fluid equations

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