All Questions
Tagged with pde fluid-dynamics
50
questions
2
votes
1
answer
211
views
Shock Capturing Methods for Shallow Water Equations
I am looking for some help finding a numerical solution to the shallow water equations:
$\partial_tu+\partial_x(u^2/2+g\eta)=0$
$\partial_t \eta+\partial_x(u\eta)=0$.
where $u$ is the depth averaged ...
- 23
1
vote
1
answer
97
views
Direct integration of 2D Euler Equations with Runge Kutta shows oscillating Courant-Friedrichs-Lewy coefficient. Stiff or Bug?
By writing the direct integration of the 2D Euler Equations in a wide and short box where the fluid enters and exits through the horizontal faces using the Runge Kutta O(4) method I have found that ...
- 113
1
vote
1
answer
191
views
Non-reflective boundary condition
I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity.
Is there any outlet boundary types that avoids the reflection of flow from the outlet back ...
- 362
1
vote
0
answers
63
views
How to numerically solve PDE that governs the free vortex wake model?
Crossposted at Math SE
I am reading a paper on the free vortex wake model for a helicopter rotor blade, which is described by the following PDE:
$$\frac{\partial \vec{r}}{\partial \psi} (\psi, \zeta) ...
0
votes
0
answers
80
views
Numerical scheme to calculate the normal mode of a set of hyperbolic PDEs?
I would like to solve the linearised, ideal, MHD equations, where the gas pressure is zero.
$$\frac{\partial u_x}{\partial t}=v_A^2(x,z)\left[\nabla_{||}b_x - \frac{\partial b_{||}}{\partial x}\right],...
- 219
1
vote
1
answer
210
views
Why is my Cahn-Hilliard simulation separating out so finely?
I am trying to simulate the Cahn-Hilliard equation using Python, but the 2 fluids aren't separating into big blobs, as desired, under any conditions. I'm setting up (what I think is) an orthogonal ...
- 11
4
votes
1
answer
152
views
Modelling flow through pipe networks
I'm trying to educate myself on modelling solute flows through pipe networks.
This is a follow up of my previous post here
$$\frac{\partial C}{\partial t} = - v\frac{\partial C}{\partial x}$$
While ...
- 433
1
vote
1
answer
365
views
How to compute turbulent energy cascade
I need to compute the kinetic energy cascade using a finite volume solution in an equally spaced grid. I wonder if it is more correct to first compute the kinetic energy in the space (or time) domain, ...
- 173
0
votes
1
answer
138
views
Well-posedness of Navier-Stokes equation
Before running a simulation for turbulence (e.g Rayleigh-Benard Convection), how do we check for well-posedness of Navier-Stokes with other equations for a given boundary condition??
Can someone ...
- 53
3
votes
1
answer
950
views
Limitations with dynamical systems vs. PDEs?
As a computational scientist, are there limitations to studying dynamical systems — systems of odes in which each state variable evolves with time — compared to studying PDEs?
For instance, it seems ...
- 31
0
votes
0
answers
55
views
Dealing with spurious oscillations in particle tracking methods
I work on modelling high intensity discharge xenon-filled lamps.
The model governing the discharge is quite complex and sadly includes fluid dynamics.
After some time, I managed to implement a finite-...
- 131
0
votes
2
answers
159
views
Second derivative in coordinate invariant form
To solve stationary, incompressible, inviscid and irrotational flow around a circular cylinder, I am using general coordinates. Since the flow is symmetrical, we only consider the upper half of the ...
- 13
3
votes
2
answers
329
views
Find classical solution of transport equation with FDM
We know the classical solution of transport equation is determined by one initial (boundary?) condition, for example, the solution of
$$\frac{\partial u(t,x)}{\partial t}+\frac{\partial u(t,x)}{\...
- 338
1
vote
1
answer
1k
views
Proper boundary conditions for potential flow around cylinder
I am computing the stationary, incompressible, inviscid and irrotational flow around a circular cylinder using a discretization in general coordinates.
I derived a PDE and proper boundary conditions ...
- 13
1
vote
0
answers
895
views
Solution to 1D consolidation problem python implementation
A solution to the 1D consolidation problem is given by
$$\frac{\partial}{\partial t} p = c_{v} \frac{\partial^{2}}{\partial y^{2}} p$$
where $p$ is the pore water pressure, $c_v$ is the ...
- 251