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Questions tagged [axisymmetry]

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NDSolve stops solving past a certain time

This is a continuation of the post I've made Unable to solve Delay PDEs Error in Boussinesq Approximation. I apologise if I shouldn't have posted a seperate question for this but I think that the ...
Lucas's user avatar
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1 vote
0 answers
82 views

Unable to solve Delay PDEs Error in Boussinesq Approximation

I'm trying to solve the set of equations below describing the flow of a pot of water being heated slightly. The equations are 2D axisymmetric in nature. ...
Lucas's user avatar
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0 answers
50 views

Piecewise Boundary Condition for axisymmetric heat equation [duplicate]

I'm trying to solve the 2D axisymmetric heat equation, where only one section of the tube is being heated up. I have written the following code below: ...
Lucas's user avatar
  • 103
2 votes
1 answer
260 views

Speeding up NDSolve to reasonable speeds to solve a coupled PDE system

Problem Statement I am planning to solve a PDE system which consists of a fluid droplet spreading on a non-Newtonian substrate. The system consists of the following equations: $$\frac{\partial p_1}{\...
FLP's user avatar
  • 547
8 votes
1 answer
567 views

Droplet of water-alcohol mixture spreading due to evaporation-caused surface tension gradient

I am trying to solve a coupled system of PDEs for 2 functions h[t,r] and c[t,r], with initial conditions of ...
James He's user avatar
2 votes
1 answer
163 views

Inactive form for PDE and symmetry

I would like to solve the following non-linear Poisson equation (as a toy problem for a more complicated problem) ...
Thela Hun Ginjeet's user avatar
1 vote
1 answer
296 views

How to calculate mean curvature of axisymmetric deformed surface?

I tried to calculate mean curvature of laser induced axisymmetric deformed surface, which radial dependence of height is given by: ...
Gopal Verma's user avatar
  • 1,065
11 votes
3 answers
1k views

Laplace's equation in spherical coordinates with Neumann b.c

I am trying to find the temperature field in a semi-infinite solid on whose surface there is an isotherm spherical cap sunken by a length p. For example: ...
umby's user avatar
  • 585
14 votes
5 answers
2k views

3D FEM Vector Potential

I am trying to reproduce an FEM result in a paper. Due to possible copyright I cannot show the result directly but fortunately there is a free link An Incomplete Gauge for 3D Nodal Finite Element ...
Greenasnz's user avatar
  • 381
6 votes
2 answers
712 views

NDSolve with equation system with unknown functions defined on different domains

Based on @xzczd's excellent answer on solving an equation system with unknown functions defined on different domains, I've tried to apply the same technique to a similar system shown below: Equations: ...
Rpj's user avatar
  • 249
2 votes
1 answer
359 views

NDSolve for system of PDEs -Error: fewer dependent variables!

I am trying to solve the equations below to find the breakthrough curve in an adsorption process: ...
Saeb's user avatar
  • 23
2 votes
3 answers
386 views

NDSolveValue taking too long

I am trying to solve heat diffusion equation on hollow cylinder with constant DirichletCondition on inner radius and zero ...
fasdgr's user avatar
  • 407
0 votes
0 answers
150 views

Ways to decrease computational time?

I have created a 2D axisymmetric simulation of the motion of charged particles in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with ...
kjcole's user avatar
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1 vote
1 answer
442 views

How to create an animation of charged particles' motion in an electric field?

I am trying to create an animation of 3 particles' motion in an electric field. The electric field is created by a needle attached to a top plate both of which are at -3800V with a grounded plate ...
kjcole's user avatar
  • 353
2 votes
3 answers
503 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 ...
Mohammad M Faghih's user avatar
11 votes
4 answers
877 views

Stress analysis in axisymmetric bodies

I would like to do some finite element calculations in axisymmetric cylindrical coordinates. I wish to calculate stress in terms of {r,z} coordinates. The radial ...
Hugh's user avatar
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2 votes
1 answer
299 views

Coupled PDEs with second order spatial derivative

I'm trying to solve a system of PDE using NDsolve but the following error accors. NDSolveValue::femcmsd: The spatial derivative order of the PDE may not exceed two. Equations: Qm and Q are ...
Hadi's user avatar
  • 21
10 votes
1 answer
848 views

Stress Operators for Finite Element Analysis

For stress analysis in the finite element method you need a stress operator. For two dimensional plane stress it can be found here. For two dimensional plain strain it can be found here. I need the ...
Hugh's user avatar
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9 votes
1 answer
396 views

Use a symmetric mesh in ListDensityPlot

I am trying to produce a ListDensityPlot but I am having issues with aliasing. The problem arises from the way that Mathematica is breaking up the mesh into ...
Kai's user avatar
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15 votes
1 answer
3k 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. ...
Foad's user avatar
  • 605
9 votes
1 answer
462 views

AceFEM: Efficient calculation of volume of axisymmetric elements

I am looking for the most efficient calculation of volume of axisymmetric elements in finite element analysis with AceFEM package. Ideally I would like to have this implemented in AceGen element code ...
Pinti's user avatar
  • 6,513
2 votes
2 answers
427 views

Plotting axisymmetric solution to transient heat equation using NDSolve

I'm having some trouble plotting my results from NDSolve in an appealing way. Below is how I tried to solve the heat equation for axisymmetric, transient diffusion in the radial direction only as a ...
Chase Kayrouz's user avatar
3 votes
1 answer
2k views

Solving two dimensional Heat equation PDE in mathematica [closed]

I am trying to solve the following equation in Mathematica but I do not know each time it only returns the equation itself instead of solving it. I tried both Dsolve and NDsolve and it was not helping ...
Silas's user avatar
  • 33
6 votes
1 answer
884 views

Meniscus outside of a cylinder - axisymmetric Young-Laplace equation in semi-infinite domain

How to solve the axisymmetric Young-Laplace equation $$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$ with b.c.s $$z'(1)=-2$$$$z'(\infty)=0$$ where $z=Z/l_c$ ...
xzczd's user avatar
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9 votes
3 answers
1k views

FEM Solution desired for "Plate with orifice" deflection: Application of Boundary Conditions and use of Regions

I found the deflection of an orifice plate (circular plate with a hole) subject to uniform pressure using Mathematica's NDSolve functionality. The plate is fixed at its outer circumference and is ...
dearN's user avatar
  • 5,351
6 votes
1 answer
1k views

NDSolve for axisymmetric problem

I would like to solve an axisymmetric Poisson equation on a disk with FEM. The code for Cartesian coordinates works fine: ...
Ivan's user avatar
  • 235
5 votes
1 answer
336 views

Revolving an axisymmetric image for volumetric rendering

I have a series of axisymmetric images of a jellyfish swimming in fluid. Overlaid on these images are plots of the Lagrangian coherent structures associated with swimming, which highlight the fluid ...
isledge's user avatar
  • 197