Questions tagged [fluid-dynamics]

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Plotting contours of a two-variable function containing a sum

I'm trying to use Mathematica to plot contours of a rather intricate two-variable function. The equation describes the velocity profile for laminar flow in a tube of rectangular section, namely: $$ {w^...
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0 answers
60 views

How to find non-trivial solution to homogeneous linear equations by Mathematica using code (Input form)?

I have many homogeneous equations to which I am interested to find the non-trivial solution using Mathematica, But I am totally new to Mathematica, so I do no know, how to find the non-trivial ...
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10 votes
2 answers
519 views

Reciprocating flow in a channel over a heated surface

The following is a coupled heat transfer and fluid flow problem. A thick plane channel is being heated with a constant flux from the bottom (at $y=-e$) with a constant heat flux $q$ as shown in the ...
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18 votes
1 answer
345 views

3D stable fluids algorithm to simulate transition from laminar to turbulent flow

This algorithm is 3D extension of our 2D algorithm published on this page and here. We suppose that with this code we can simulate transition from laminar to turbulent flow. In this example we compute ...
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4 votes
1 answer
145 views

How to display warning message inside manipulate?

Using the code shown, Reynolds number is calculated for given parameters. Is it possible to display a warning message to the user if a parameter is outside applicable range? e.g., if the fluid ...
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Can mathematica numerically solve this system of coupled integro differential equations?

Here's my system: R(x,y,t) is the concentration of a chemical that's diffusing across the box. The disk is a mobile sink for the chemical, which absorbs it in proportion to its concentration. The ...
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1 vote
0 answers
75 views

Interaction between fluid flow and elastic obstacle (fluid-structure interaction) [closed]

I would like to model the velocity and pressure distribution of an elastic obstacle in a channel where the fluid flows. There are Navier-Stokes examples in Mathematica webpage with rigid obstacles but ...
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1 vote
1 answer
83 views

How to make a calculator to display the Non-Dimensional number

I am a beginner here and want to learn this tool. At first, I want to make one calculator that will display the value of the Non-Dimensional number of Fluid dynamics based on user inputs. In this code,...
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5 votes
2 answers
233 views

Modified Heat Transfer in Fluid Flow

I am trying to simulate Modified Heat Transfer in Fluid Flow (based on Buoyancy-Driven Flow in a Square Cavity ). The modified heat transfer takes the form: with the solid volume fraction: The ...
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18 votes
1 answer
438 views

Stable fluids code for electromagnetic mixture application

This code has been translated from the original Jos Stam code and improved with some Mathematica functions. It solves problem of viscous incompressible flow with electromagnetic force in a rectangle ...
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12 votes
1 answer
560 views

Stokes equations in 2D with traction boundary conditions

This is a follow-up to a previous question (see here). We would like to solve the two-dimensional Stokes equations using the FEM package in Mathematica, when we prescribe traction boundary conditions. ...
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4 votes
1 answer
386 views

Stokes equations in 2D with Neumann conditions

I would like to solve the 2D Stokes equations within a unit disk, say $\Omega$, by using the finite element method (FEM) as it is implemented in NDSolve (by loading ...
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1 vote
1 answer
60 views

How to find invariant sets of nonlinear operators below

How to find invariant sets of nonlinear operators below. $$x[n+1]=0.9∗y[n]^2/(y[n]+2)+x[n]∗(1−0.8/(1+x[n]))$$ $$y[n+1]=0.8∗x[n]/(1+x[n])+0.6∗y[n]$$
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4 votes
2 answers
202 views

2D incompressible flow solver with known non-zero initial velocity distribution

I know that there are lots of questions on this forum regarding mathematica FEM, but I haven't quite found what I am looking for. I will be working with data obtained through PIV (particle image ...
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0 answers
66 views

How to solve this linear complementarity problem with NDSolve or other functions? The arguments should be ordered consistently

I want to find a numerical solution of $\omega(t,q)$, where $t\in[0,T]$ and $q\in[0,N]$. $q_t$ is a determinstic w.r.t $t$, other unmentioned parameters can be fullfilled or given by the user. I met ...
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0 answers
71 views

Nonlinear Differential Equation with Paramaters in Sqrt Function

For a university project, I am trying to see if my system will have choked flow and also plot the resulting pressure spike. I set up the system below to try to model the transient response. I am able ...
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1 answer
76 views

Using Solution to Differential Equation in New Function

I am trying to feed the solutions from my differential equations into another function. I am using NDSolve to solve two differential equations simultaneously. It ...
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6 votes
0 answers
175 views

System of coupled nonlinear pdes with FEM (magneto-hydrodynamic mass transfer)

EDIT 01 See end of post for an update. Original Question I'm trying to reproduce the magneto-hydrodynamic flow studied here using the nonlinear FEM functionality, and have been having trouble ...
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0 votes
1 answer
162 views

FEM analyis of flow in a hydrocyclone [closed]

I am interested in solving the flow in a hydrocyclone (steady Navier Stokes equation). I have an STL file of the 3D geometry. My question is how to extract the internal geometry of the hydrocyclone ...
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0 votes
2 answers
108 views

Better method for computing streamlines

Can someone suggest a better way to solve for streamlines? P.S. StreamPlot is not providing accurate results. Here, velocity is...
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0 answers
90 views

please help me .. can any one solve this problem usingg NDSolve [duplicate]

solve for dependent variable f and theta. where m and n are parameters please help me. ...
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0 votes
1 answer
143 views

How can i solve and plot this non linear ODEs usin NDSOLVE?

I am trying to solve the following non-linear ODEs ...
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7 votes
2 answers
848 views

Cylindrical coordinates in FEM

I am trying to solve the Stokes equation for fluid flow in a 3d cylinder. All boundaries are no-slip, apart from the top boundary, which enforces flow in the x-direction. My problem is that I can't ...
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11 votes
4 answers
720 views

Area/Volume of a 2D/3D object as it is filled up with water

How could I get the volume of water on a region as it is filled up with water from below? Assume gravity points in some appropriate downward axis like -y (or -z in 3D) so the water fills upward from ...
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6 votes
1 answer
324 views

FEM: periodic solution of 2D Navier-Stokes equations

Let’s consider a horizontal channel with a round obstacle in the middle. ...
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9 votes
1 answer
556 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 ...
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16 votes
2 answers
1k 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'...
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2 votes
3 answers
333 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 ...
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4 votes
0 answers
190 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 ...
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8 votes
1 answer
387 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 ...
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5 votes
1 answer
408 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}...
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1 vote
0 answers
230 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 ...
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3 votes
1 answer
110 views

Solving a System of Differential Equations for Pendant Drop Application [duplicate]

So I'm trying to solve the system of differential equations describing a pendant drop. The system is as follows: ...
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1 vote
1 answer
43 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 ...
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0 votes
2 answers
132 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=...
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9 votes
2 answers
846 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! ...
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1 vote
1 answer
284 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 ...
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15 votes
1 answer
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. ...
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1 vote
0 answers
729 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 ...
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0 votes
1 answer
181 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 ...
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  • 1
0 votes
1 answer
242 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 ...
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3 votes
1 answer
604 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 ...
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  • 585
0 votes
2 answers
500 views

Stokes' second problem [closed]

I'm trying to solve this equation ...
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  • 1
1 vote
1 answer
471 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. ...
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3 votes
0 answers
1k 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 ...
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  • 519
5 votes
1 answer
583 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 ...
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3 votes
0 answers
535 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 ...
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2 votes
0 answers
186 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 ...
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1 vote
0 answers
377 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 ...
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  • 1,233
10 votes
1 answer
479 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 ...
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