Linked Questions

11 votes
1 answer
5k 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 ...
sasa's user avatar
  • 127
56 votes
3 answers
6k views

Mathematica vs. Comsol for finite element analysis?

Being relatively new to finite element analysis, I was wondering how expert users assess Mathematica's capabilities in solving PDEs via the finite element method compared to other commercial tools (e....
Alexander Erlich's user avatar
21 votes
4 answers
6k views

How do I solve a PDE with a strange boundary condition?

How do I solve the PDE with boundary value like this $$u(t,x,y)=0, \textrm{when } F(x,y)=0$$ using DSolve? As a specific example, I want to solve heat equation $$\frac{\partial u}{\partial t}=\...
Golbez's user avatar
  • 313
9 votes
2 answers
5k views

Solving a nonlinear PDE with Mathematica10 FEM Solver

I am trying to solve a system of coupled nonlinear PDEs in a rectangular region with the new FEM solver in Mathematica 10. However, I come across an error stating NDSolveValue::femnonlinear: ...
Oscillon's user avatar
  • 1,241
18 votes
1 answer
2k views

Solver for unsteady flow with the use of the Navier-Stokes and Mathematica FEM

There are many commercial and open code for solving the problems of unsteady flows. We are interested in the possibility of solving these problems using Mathematica FEM. Previously proposed solvers ...
Alex Trounev's user avatar
  • 45.4k
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
8 votes
2 answers
752 views

Solving a coupled nonlinear PDE using low level FEM programming

Inspired by user21 we try to solve this diffusion reaction problem using low level FEM we start defining a mesh and the utility function ...
LinearLambda's user avatar
9 votes
1 answer
658 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 ...
M.R.'s user avatar
  • 31.5k
10 votes
2 answers
1k views

Stiff BVP of nonlinear ODE, alternative/ enhancement to shooting method

Question: I have been trying to solve this coupled ODE set. \begin{align} ( \frac{ \mu^2}{B} +1 ) \Phi^2 + \frac{1}{A} {\Phi^{\prime 2}} + \frac{1}{2}\lambda \Phi^4 - \frac{A'}{r A^...
Boson Bear's user avatar
5 votes
3 answers
835 views

Non-linear Poisson equation over non-rectangular domain

I need to solve non-linear Poisson equation Laplacian[u[x, y], {x, y}] == u[x, y]^2 Over a non-rectangular domain The problem in short: non-linear Poisson ...
Maxim Lyutikov's user avatar
11 votes
1 answer
675 views

Solving a system of temporal non-linear (reaction-diffusion) PDEs over a region using Neumann conditions

I am trying to solve a system of PDEs with non-linear terms: $\frac{\partial a(x,y,z,t)}{\partial t}=\color{red}{-\text{$\tau_2 $ } a(x,y,z,t) h(x,y,z,t)}+\text{$\tau_1 $ } d(x,y,z,t) \\\frac{\...
Ruud3.1415's user avatar
3 votes
1 answer
788 views

Derivative on uneven grid using interpolate

I have a following problem: I have an uneven 2D grid of points with unknown function value. Let's take some nasty region: ...
user16320's user avatar
  • 2,396
2 votes
2 answers
302 views

Solving non-linear PDEs

I wish to solve the equation $$\frac{dp(x,y,t)}{dt} = D\ \nabla^2 (p(x,y,t)) -C \ p(x,y,t) - R \ p(x,y,t)^2 $$ But, I get the error ...
Tomi's user avatar
  • 4,438
2 votes
0 answers
484 views

Solve vs. LinearSolve - ill solutions using both methods [closed]

I'm wishing you a nice day. My question is related to this question previously asked by me, answered by PlatoManiac. Although I found a bug in his post I decided to leave his answer accepted and ask ...
user16320's user avatar
  • 2,396
3 votes
0 answers
346 views

Solving nonlinear PDE in Mathematica [closed]

I want to solve the nonlinear PDE for the anisotropic fluid flow: $(C_{ijkl}v_{k,l})_{,j}-p_{,i}-v_jv_{i,j}=0$ Mathematica can solve it without last nonlinear term with the following code (using ...
Данил Семёнов's user avatar

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