Questions tagged [fluid-dynamics]
The fluid-dynamics tag has no usage guidance.
35
questions
7
votes
1answer
322 views
How to create a fluid animation like this?
When two fluids move past each other at different speeds, complex instabilities arise that look really cool:
The Navier-Stokes equations are numerically intense but can usually predict what will ...
14
votes
2answers
279 views
Plotting Joukowski Airfoil Streamlines using conformal maps
I want to plot the streamlines around Joukowski Airfoil using conformal mapping of a circle solution.
I do know that there are a lot of solutions to plot the airfoil itself (for example this), but I'...
1
vote
3answers
207 views
Non-Newtonian Momentum Eqn in a rectangular pipe
I am trying to (numerically) solve the momentum eqn for a non-Newtonian fluid in a pipe with rectangular cross section using Mathematica.
Here are the assumptions:
So, the flow is only in z ...
4
votes
0answers
134 views
Interactive CUDAFluidDynamics example without CUDA?
On Macbooks OpenCL works but not CUDA. I saw this fun example CUDAFluidDynamics in the CUDALink package and I wanted to play with it, but couldn't.
Perhaps someone ...
7
votes
1answer
204 views
Curved Dirichlet boundary in FEM
Based on this fascinating blog post (https://blog.wolfram.com/2013/07/09/using-mathematica-to-simulate-and-visualize-fluid-flow-in-a-box/) from a few years ago that shows how to simulate a driven ...
4
votes
1answer
178 views
Solving the Stokes equation for planar Marangoni flow with FEM
Background
I would like to numerically solve the stationary Stokes equation from fluid dynamics
$\eta_i \nabla^2 \vec{u}_i - \nabla p = 0$
with the incompressibility condition
$\nabla \cdot \vec{u}...
0
votes
0answers
143 views
How to animate this fluid flow over airfoil?
I found this website very interesting "http://bugman123.com/FluidMotion/index.html" here he provided various animations of fluid flow and some codes are given in Mathematica. I found this animation of ...
2
votes
1answer
58 views
Solving a System of Differential Equations for Pendant Drop Application
So I'm trying to solve the system of differential equations describing a pendant drop. The system is as follows:
...
1
vote
1answer
37 views
Dynamically update 2D configuration - Data from file
I'm trying to simulate the evolution of a classical fluid in 2D. I have a file that contains the evolution of a configuration of points in a 2D, with a white line between each "snapshot". For 3 ...
0
votes
2answers
83 views
Get the 2d plot of the intersection of 3d surfaces
I am trying to find points $(x,y)$ which satisfy the following constraint:
$$1000F_r(x,y)=\frac{1000x\sqrt{1/y^2-1/A^2}}{1+x\sqrt{1/y^2-1/A^2}}=1/2$$
Where $A\simeq0.0008$. My idea was to plot $z=...
7
votes
2answers
355 views
Analytic solution to Orr-Sommerfeld-Squire equations for a special case
Hello everybody in Mathematica SE. Although my question is related to flow stability analysis, this should be a general application of MMA to solve a system of ODEs. Thank you for your suggestion!
...
1
vote
1answer
161 views
Dual solution of nonlinear ordinary differential equations [closed]
As we know, we can solve nonlinear ordinary differential equations arising in fluid dynamics using Mathematica command NDsolve. But, now I want to find the dual ...
13
votes
1answer
2k views
Solving Navier-Stokes equations for a steady-state compressible viscous flow in a 2D axisymmetric step
Note: you may apply or follow the edits on the code here in this GitHub Gist
I'm trying to follow this post to solve Navier-Stokes equations for a compressible viscous flow in a 2D axisymmetric step. ...
0
votes
0answers
455 views
I am having trouble solving a nonlinear ODE with Homotopy Analysis Method using BVPh2 package on Mathematica
I have the following equations after performing the similarity transformation on fluid dynamic equations.
$f'''+ff''-2f'^2-Mf'-G_rg=0\\(1/P_r)g''+g'f-Rg + \delta Exp[g/(1+\epsilon g)]=0 $
I have 5 ...
0
votes
1answer
143 views
How to solve the following system with NDSolve and FindRoot? Please address
Consider the following coupled systems of equations
$f′′− k^2 f=k\, \mathbf{Ra}$ and $g′′− k^2 g=k\,f$ , where $f$ and $g$ are functions of $z$. The boundary conditions for the problem are $f=0$ and ...
0
votes
1answer
194 views
Bifurcation diagrams
I'm trying to get the Bifurcation diagrams for u, v, w, s, f, g and h as function of r
I got some kind of code to do this, but I do n't have any idea of what is going on with code and i'm getting ...
3
votes
1answer
409 views
Solving a system of partial differential and algebraic equations? setting the step-size to get reasonable results
I'm trying to use Mathematica to get some early approximate solutions to a system of algebraic and partial differential equations. It is actually 1D model of an ideal gas in a tube. I'll divide my ...
0
votes
2answers
375 views
1
vote
1answer
232 views
Integration and plotting: How to draw Pathline?
I have function $u_x = dx/dt = 5 - (0.5y)/(x^2+y^2)$
and $u_y = dy/dt = (0.5x)/(x^2+y^2)$
and I'm trying to integrate pathline equation with respect to $t$ at reference point at $(-0.3,0)$ at $t= 0$s.
...
3
votes
0answers
753 views
How to visualize the vorticity of a 3D velocity field? [closed]
I sample a snapshot from a system with 50 particles including their position and instant velocities.
The snapshot is a list of 3 position and 3 velocities values per particle. i.e. 50 lines each of ...
5
votes
1answer
429 views
Position dependent Neumann condition on boundary mesh
I am trying to solve Laplace equation over a time-dependent region using cylindrical coordinates. My system is independent of the angle coordinate, and so the equation looks like:
The region ...
3
votes
0answers
409 views
Solve PDE over time-dependent region
I have some experience with C++ programming, but I am quite new to Mathematica and I think the latter requires a different mindset which I am still not used to.
I would like to simulate the effect ...
2
votes
0answers
157 views
cdf player poiseuille flow
i am trying to model the dynamic behavior of a micropolar fluid. From the equations of motion we derive the analytical solution for the fluid velocity which is
I am interested only in u(y). I found ...
1
vote
0answers
240 views
Find streamfunction manually from numerical velocity field
I have a discrete two-dimensional velocity field $(u,v)$ given by (as an example)
Table[{Sin[i], Cos[i]}, {i, 0, 8 \[Pi], 0.5}, {j, 0, 8 \[Pi], 0.5}]
I can plot ...
10
votes
1answer
361 views
Simplify fluid flow by using symmetry property
I am trying to describe the fluid flow within a radially symmetric tube and use the code as it can be found from Wolframs homepage as template (Stokes's equation).
I adapted the geometry and the ...
3
votes
2answers
611 views
How to animate multiple sets of XY data
I have nine sets of data with $(x,y)$ coordinates that are the position of a particle. I can ListPlot the particle positions on a single plot, but, I want to ...
2
votes
1answer
202 views
StreamPlot use fixed integration time to determine final path length, not fixed path length
I'm plotting velocity fields for fluid flow, and my call to Streamplot looks something like this:
...
0
votes
1answer
336 views
DSolve Error 3D Navier Stokes (z,r,t)
I am essentially wanting to solve Navier Stokes in the [z,r,t] dimensions (2D+Unsteady Flow) for pressure driven flow. However, I keep getting an error I am unable to resolve in my Dsolve such as:
...
5
votes
2answers
632 views
Postprocessing of CFD results in Mathematica
I was trying to perform computational fluid dynamics (CFD) post-processing in Mathematica after solving primitive variables from Navier-Stokes equation, mainly $(u,v)$, $(Px,Py)$. Since I am not an ...
7
votes
2answers
601 views
Von Kármán Vortices
How may we vary vectors in
StreamPlot[{y, -Sin[x/2]}, {x, -4, 12}, {y, -4, 4},
StreamColorFunction -> "Rainbow", AspectRatio -> Automatic]
to obtain a ...
9
votes
2answers
2k views
How can I use ContourPlot to creat streamline: proper arrow orientation and correct domain?
I get into trouble when I use ContourPlot to draw streamlines in a free surface flow domain.
This is my data.The data are a little bit big, please be patient.
Here ...
10
votes
1answer
3k views
How to solve fluid flow problem based on Navier-Stokes equations? [duplicate]
Does anyone know or can provide any examples how fluid flow problem can be formulated and solved in Wolfram Language? Simplest cases of 1D or 2D flows based on Navier-Stokes equations or even their ...
8
votes
1answer
797 views
Circumvent NDSolve::bdord: error for 1-D Euler Equations
I attempted to use NDSolve for the 1-D isentropic unsteady flow equations with low subsonic inflow velocity and prescribed inflow total enthalpy; along with a non-...
8
votes
1answer
2k views
Mathematica code for solving MHD viscoelastic fluid flow
Where might I find Mathematica code for solving MHD viscoelastic fluid flow using Homotopy Analysis method?
10
votes
2answers
4k views
Singularities using VectorPlot
I am trying to plot a vector function of a fluid flow given by
$\vec{V} = (\frac{-\cos(\theta)}{r^2},-\frac{\sin(\theta)}{r^2})$
I am trying to plot it in Mathematica using the command below, I ...
