# Questions tagged [fluid-dynamics]

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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 ...
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'...
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 ...
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 ...
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 ...
178 views

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! ...
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
375 views

### Stokes' second problem [closed]

I'm trying to solve this equation ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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: ...
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 ...
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 ...
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 ...
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 ...
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-...
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 ...