Linked Questions

25 votes
2 answers
3k views

I failed to solve a set of one-dimension fluid mechanics PDEs with NDSolve

The fluid here has been assumed as single component perfect gas i.e. it obeys the equation $p=ρ R T$, the thermal conductivity is assumed as a constant, so the equation set is: ...
xzczd's user avatar
  • 67k
16 votes
2 answers
3k views

Boundary condition with spatial derivative is ignored by NDSolve

Consider the following differential equation: $$\begin{align*}&\rho C_p\left(\frac{\partial T}{\partial t}\right)=k\left[\frac{\partial^2 T}{\partial x^2}\right]+\dot{q}\\ &\text{at }x=0,\;\...
Feyre's user avatar
  • 8,617
22 votes
2 answers
1k views

NDSolve uses different difference order for different spatial derivative when solving PDE

I found something this tutorial for method of line doesn't tell us. Consider the following toy example: ...
xzczd's user avatar
  • 67k
6 votes
2 answers
475 views

Solving linear coupled PDEs by FDM

I am trying to solve some linear, coupled PDEs for perturbative analysis (first order in time, 3rd order in space), for which I then plan to take the global spatial maxima of their magnitudes and plot ...
user213068's user avatar
2 votes
2 answers
745 views

Solving 2D+1 PDE with Pseudospectral in one direction with periodic boundary condition?

According to the documentation about the pseudospectral difference-order: It says: Following the discussion here: I found the messy behavior is always on the artificial boundary in $\omega$-...
Bob Lin's user avatar
  • 445
5 votes
1 answer
324 views

How to solve a 2D+1 PDE with a large convection term in stable and efficient way

Follow from the discussion 2D+1 PDE problem $\partial_t u(t,x,y)=-y\partial_{x}u+\partial_{y}\left[γ(1+sin(3x)) yu+A sin(3x)u+γkT(1+sin(3x))\partial_{y}u\right]$ with $u(0,x,y)=\frac{1}{2\pi}e^{-(x^...
Bob Lin's user avatar
  • 445
0 votes
1 answer
318 views

How to solve 2D PDE with a constraint?

As related to the 2D+1 PDE problem, if now I would like to solve the stationary solution which satisfies $\partial_t u(t,x,y)=0$. Or equivalently, $-y\partial_{x}u+\partial_{y}\left[a y+b sin(x)u+...
Bob Lin's user avatar
  • 445
1 vote
1 answer
162 views

Solution distorsion after long time evolution for 2D+1 PDE [closed]

Continue the discussion 2D+1 PDE problem. Why the solution eventually becomes messy and show those warning messages. Here is the code: ...
Bob Lin's user avatar
  • 445
0 votes
1 answer
179 views

Inconsistent of initial and boundary condition in 1D PDE

I am now dealing with the 1D PDE with periodic boundary condition given by the following: $$ \partial_{t}u(t,x) = \partial_{x}u(t,x). \quad \text{with}\quad u(0,x)=\frac{1}{\sqrt{2\pi}}e^{-(x-\pi/4)^...
Bob Lin's user avatar
  • 445
0 votes
1 answer
145 views

NDSolveValue gives an error that a list of equations is expected

I have this system of PDE that I want to solve. I reduced my original system of PDEs to the system below to capture the error (the actual code is after the image at the buttom): Function ...
MOON's user avatar
  • 3,876