Questions tagged [fluid-dynamics]
The study of the properties of fluids and gases in motion
524
questions
3
votes
1answer
238 views
Stability Criterion for this Explicit Scheme
I am solving an unsteady flow using the dual-time Navier-Stokes equation in which I write my momentum equation as:
$$\frac{\partial u}{\partial \tau} + \frac{\partial u}{\partial t} + \frac{\partial u^...
3
votes
2answers
461 views
Stagnation or Total conditions in a pipe with moving fluid?
In Flow Science, they provide an example of boundary conditions and how to specify them for CFD simulations. The following is stated:
Pressure Boundary Example
For example, consider the ...
3
votes
1answer
186 views
LU-SGS and boundary conditions
I am trying to understand how boundary conditions are implemented when one uses the nonlinear LU-SGS algorithm for Euler equations. Most papers describe the Gauss-Seidel sweep over mesh cells, but do ...
3
votes
1answer
373 views
Finite difference scheme for 2D sound propagation
I am simulating the sound wave propagation in non-rectangular and asymetric spaces using finite-difference method. I presume linear acoustics equations to be enough (i.e. $\Box p = 0$, $\Box \vec{v} = ...
3
votes
1answer
690 views
2D Poisson Solver for Taylor Green Vortex Problem
I am trying to write a 2D Navier Stokes solver using an RK3 for time advancement in python. For debugging, I have converted the RK3 to an Euler step for simplicity. Checking my divergence for my ...
3
votes
1answer
360 views
Finite Element integration with tensor notation
While I was studying discontinuous finite element methods I found an integration of a Navier Stokes equation using tensorial notation. The equation is the following:
$\mathbf{\bar {u}}_{t} + (\...
3
votes
1answer
218 views
Non-linear ordinary differential equation in the modeling of the oscillation of a meniscus
I am trying to model the oscillation of a fluid miniscus in a straw when the miniscus is displaced from its equilibrium level. The results was the following non-linear ODE:
$$y''= 1/y - 1.$$
This ...
3
votes
1answer
153 views
Transient Fluid Dynamics
Eventually, I would like to numerically simulate the transient compressible flow in an axial compressor during start-up.
However, I know that this is a very challenging undertaking (to say the least).
...
3
votes
1answer
295 views
CFD (Fluent) define a inlet for a tidal basin
I'm still pretty new in the CFD modelling world.
Can anyone advise me how to define a inlet for a tidal basin in Fluent?
The water level and the velocity at the inlet vary in time due to the tide ...
3
votes
0answers
57 views
Is it possible to shift the numerical results in order to compare it with the analytical solution?
I'm using lattice Boltzmann method (LBM) to do simulation of flow in a pipe. The diameter of the pipe is 0.02 m and its height is 0.1 m. I put a parabolic velocity profile at the inlet:
$$\mathbf{u}(\...
3
votes
0answers
55 views
Choosing good modelling method for solving Boltzmann equation
I'm writing a solver for Boltzmann Equations (BE) including a force term in rarefied plasma, for my PhD. The aim is to see if an instability occurs inside an electric streamer (theoretically it should,...
3
votes
0answers
88 views
Is the matrix exponential and the Jordan canonical form actually useful for solving differential equations?
All of my yearlong graduate-level Linear Algebra course notes from my professor—an algebraist/representation theorist—shows his love for the exponential map $e^A$ and the Jordan canonical form—and one ...
3
votes
0answers
88 views
numerical instabilities in Fluid Dynamics, Finite Element Method
I'm looking for references to understand where the numerical instabilities come from in hydrodynamics in general, and notably when the Péclet number: $Pe>1$. I'm using the finite element method.
...
3
votes
0answers
66 views
Should I expect computational gains using a second-order splitting method here?
I am trying to solve a three-dimensional baroclinic transport problem. The hydrodynamic (three-dimensional shallow water) equations are:
\begin{align}
\nabla \cdot \vec{v} = 0, \tag{1} \\
\frac{\...
3
votes
0answers
196 views
Finite Element Stabilization for Drift-Diffusion/Advection-Diffusion Equations
I've tried my best to look through the relevant suggested similar questions when posting this, and hopefully this contains enough new material to not be considered a duplicate.
I'm currently trying ...
3
votes
0answers
145 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
votes
0answers
275 views
Simulation of surface tension-dominated interfaces
I want to simulate the shape of the free surface in a small fuel tank in microgravity, which is very slowly being emptied.
The tank is not symmetric, the geometry is given by CAD (e.g. step file).
...
3
votes
1answer
96 views
Computational Fluid Dynamics: Question on a third-order accurate finite difference approximation
According to this paper the following finite difference approximation is third-order accurate:
$$\frac{d\rho_j}{dx}\approx\frac{2-\eta}{3}\frac{\rho_{j+1/2}-\rho_{j-1/2}}{\Delta x}+\frac{1+\eta}{3}\...
3
votes
1answer
447 views
1-D turbulent energy spectra in homogeneous direction (non-isotropic)
I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
3
votes
0answers
194 views
Rhie--Chow interpolation on PDE level
The Rhie--Chow [1] interpolation seems to be a standard tool in the Finite-Volume discretization of incompressible flows.
It is commonly defined on the discrete level [2].
In the lecture notes [3] --...
3
votes
0answers
72 views
Cavity Flow CFD Boundary conditions and strange waves
So I have a PDE that I use to describe how material flows through a volume(2D or 3D).
$$\frac{\partial C}{\partial t} + \vec{u} \cdot \nabla C = (D' + D )\nabla^2C$$
Now using finite differences I get ...
3
votes
0answers
324 views
Collocated Grid Navier Stokes Solver
I want to solve Navier Stokes equations on a collocated grid. Earlier, I was using a MacCormick scheme based solver where I discretized predictor step in forward differences and corrector step in ...
3
votes
3answers
1k views
Time step size for transient simulations of vortex shedding
I am simulating unsteady flow around a circular cylinder (using FLUENT). I am facing the following problem. Kindly please help me.
OBJECTIVE:
To find out the Reynolds number at which vortex shedding ...
3
votes
0answers
294 views
Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation
My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
3
votes
0answers
358 views
Euler Equation Eigensystem with Gravity in the Energy Flux
I am modifying a conservative form of the Euler equations with gravity in the energy flux (see previous question: Energy Conservation in Conservation Laws with Source Terms) for use in a Riemann ...
3
votes
0answers
55 views
Discretizing boundary conditions for vortex methods
I am working on a fluid simulation using vortex methods. For this I must compute the vortex sheet on my boundaries given as:
$$
\gamma(\mathbf{x}) - \frac{1}{\pi}\int_S \frac{\partial}{\partial\mathbf{...
3
votes
0answers
359 views
Transport Equation in a Tube: Source Term on Boundary
I'm modeling mass transport in a flow reactor. The flow reactor is a tube, which allows me to use cylindrical symmetry in solving the Convection-Diffusion-Reaction (CDR) Equation, which governs the ...
3
votes
0answers
640 views
Immersed boundary method
I'm trying to use immersed boundary method for the 3D flow problem (Navier-Stokes equations), but I'm maybe misunderstood something in this method. Main principles I took from this book. I use the ...
3
votes
0answers
243 views
N-body simulation for particles
I would like use N-body simulation for measure a torque on an object in a liquid (helium). It's a 2D study. On the site : http://www.browndeertechnology.com/docs/BDT_OpenCL_Tutorial_NBody-rev3.html I ...
3
votes
0answers
213 views
How to estimate if a velocity field is statistically homogeneous?
For a 3D velocity field $\mathbf{u}$ obtained by direct numerical simulation.
Assuming that the field is defined on a periodic domain $\mathcal{P}$ of periodicity $L_x$ in the $x$ direction, $L_y$ ...
3
votes
1answer
410 views
General case Kutta condition
I'm working on a 2D inviscid fluid simulation using a "panel method", with Potential being used to enforce the no-through boundary condition. I'm trying to incorporate the Kutta condition, which says ...
3
votes
0answers
2k views
Create 2D plot from two data sets in ParaView
I'm currently running a CFD simulation for an internal flow and need to compare my computed results to experimental data. The experimental data is saved as a comma separated file with columns for x,y,...
2
votes
3answers
1k views
2D Stokes equation Code
Does anyone know where could I find a code (in Matlab or Mathematica, for example) for he Stokes equation in 2D? It has been solved numerically by so many people and referenced in so many paper that I ...
2
votes
1answer
4k views
What's the difference between grid-based and mesh-based methods for PDEs?
I am into computational fluid dynamics and so far I've found that the most common approaches to solve for the governing equations are Eulerian and Lagrangian. The former samples the domain at fixed ...
2
votes
1answer
223 views
What is eighth order central difference?
The origin of the question can be found here.
I know the details about forward, backward and central differences.
If $u$ is the variable, does eight order means it approximates the $u_{xx}$ using $u$...
2
votes
2answers
375 views
2d Euler manufactured solutions
Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?
2
votes
2answers
173 views
Why have specialised upwind schemes been developed to solve hyperbolic equations?
Are upwind schemes such as Godunov type methods superior to central differencing schemes? Do the reasons include superiority in modelling hyperbolic problems with Dirichlet BC's?
2
votes
2answers
179 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 ...
2
votes
3answers
145 views
combination of field and particle methods for fluid dynamics
In numerical fluid dynamics there are field methods like finite-volume, finite-element, etc. and particle methods like Smoothed-Particle-Hydrodynamics – SPH and others. Both approaches have advantages ...
2
votes
2answers
136 views
Expected computational time for DNS computation of fluid flow
Using an established criterion involving capturing eddies down to the Kolmogorov length scale it can be reasoned that the order of grid points in the computational mesh needs to be $N^3 \ge Re^{9/4}$ ...
2
votes
2answers
656 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 ...
2
votes
2answers
313 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 ...
2
votes
1answer
505 views
What are acceptable boundary conditions for porous media flow?
I am attempting to simulate fluid flow through a porous foam. I would like to have no-slip boundary conditions on part of the boundary and free flow conditions on the inlet and outlet. Right now I am ...
2
votes
2answers
2k views
Patankar's algorithms for Numerical Heat Transfer and Fluid Flow
I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
2
votes
1answer
211 views
Physical interpretation of divergence theorem
In a diverging pipe section like the following,
the pipe of radius $r$ splits into two pipes of radius $r/2$.
Consider a solute transported by convection from node 1.
$$\frac{\partial C}{\partial t}...
2
votes
4answers
914 views
Simple methods for solving 2D steady incompressible flow?
I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 ...
2
votes
1answer
637 views
Basic Finite Element Method (FEM) question: assembly and re-assembly
I'm reading up on the Finite Element Method (Zienkiewicz's Book), so I understand better what I'm doing in FEniCS and COMSOL. Currently, I'm wondering about this:
Using FEM to solve fluid flow ...
2
votes
2answers
1k views
Vortex Panel Method implementation
I'm trying to understand and implement panel methods for a two-dimensional airfoil.
I haven't found yet a very detailed explanation on how to implement it, and there are some things I don't' still ...
2
votes
3answers
185 views
How is central difference scheme second-order accurate?
In an arbitrarily unstructured mesh, shown in the figure below, in the context of finite volume method, I want to obtain an approximation of $\phi_f$, where $N$ and $P$ are cell centers of adjacent ...
2
votes
1answer
92 views
Confusion about Zabusky and Kruskal's stepper for the KdV equation
In Zabusky and Kruskal's paper about solitons, they derive the following update for the Korteweg de Vries equation (their footnote 6):
\begin{align*}
u_{i}^{j+1} = u_{i}^{j-1} - \frac{1}{3} \frac{k}{...
