All Questions
Tagged with computational-physics finite-difference
27
questions
2
votes
1
answer
278
views
Asking advice for implementation of Conservative Finite Difference Scheme for numerically solving Gross-Pitaevskii equation
I am trying to numerically solve the Gross-Pitaevskii equation for an impurity coupled with a one-dimensional weakly-interacting bosonic bath, given by (in dimensionless units):
\begin{align}
i \frac{\...
- 21
1
vote
1
answer
107
views
Isolating decaying solutions to nonlinear second-order ode
I need to solve a nonlinear ODE of the form
$$
\frac{d^2 y}{dx^2} + \frac{1}{x}\frac{dy}{dx}-\frac{1}{x^2}\sin(y)\cos(y)+\frac{2}{\alpha}\frac{\sin^2(y)}{x}-\sin(y)=0
$$
numerically, subject to the ...
- 11
1
vote
0
answers
62
views
Need help implementing finite difference Beam Propagation Method to Solve 2-D Helmholtz equation
I am trying to implement beam propagtion method in a two-dimensional lattice to solve Helmholtz equation by following the scheme given this paper. I am using Matlab for implementation.
The expected ...
- 11
2
votes
0
answers
176
views
Poisson equation solution in a semiconductor structure
I am trying to solve the $\textbf{1-D}$ Poisson equation for a semiconductor structure at equilibrium (There is no external bias applied).
$\textbf{Background}$
\begin{equation}
\frac{d^2V}{dx^2} = -\...
- 33
1
vote
0
answers
207
views
Solving PDE on a non-uniform grid with Crank-Nicolson scheme
I am solving a 1D diffusion-type equation with the finite-difference Crank-Nicolson (CN) scheme, and I need to densify the spatial grid around the central point. One could change the spatial variable ...
- 21
0
votes
1
answer
218
views
What's Kane S. Yee who invented FDTD in Chinese?
I'm not sure if the question suits this section of StackExchange, but I think the chance to get the answer is highest here (compared with other forums). So I hope more tolerance could be shown towrad ...
- 302
2
votes
0
answers
45
views
Calculating the species mass consumption from implicit reaction-term in diffusion-reaction equation
The 1D diffusion equation with a chemical source term has the following form:
$$\frac{\partial Y}{\partial t} = D \frac{\partial^2 Y}{\partial x^2} - k Y,$$
where $Y$ is the molar concentration of the ...
- 21
-1
votes
1
answer
154
views
The local and average Nusselt number in a square cavity
I am in the process of programming the local & average Nusselt number in a left vertical wall but my Matlab script gives me inappropriate values and it doesn't change with changing of Rayleigh ...
- 1
0
votes
1
answer
188
views
Computing eigenvalues of Schrodinger equation with spin
I want to solve a 2-dimensional particle in box problem with two electrons in the quantum well.I would like to take into account spin of electrons and Coulomb interactions to compute singlet and ...
- 21
1
vote
0
answers
425
views
How to compute the Eigenvalue and Eigenstates of Quantum well with Effective mass using finite difference method in Python?
I want to compute the eigenvalues and eigenstates of a quantum well with different effective masses of electron in the barrier and in the quantum well. As can be seen [1]: https://github.com/mholtrop/...
- 21
1
vote
0
answers
177
views
Integrating a wavelike equation with absorbing boundary conditions
I am trying to numerically solve the following equation:
$\frac{\partial^{2} \phi}{\partial t^{2}}-\frac{\partial^{2} \phi}{\partial x^{2}}+V(x) \phi(x, t)=0$ On some domain, with:
$\phi(x, 0) = I(x)$
...
- 111
9
votes
4
answers
698
views
Finite-difference software for solving custom equations
Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as ...
- 201
2
votes
1
answer
132
views
Effect on methods like Crank-Nicolson of adding a potential term, changing heat equation to Schrodinger equation
I'm studying up on methods for numerically solving the Schrodinger equation. The Schrodinger equation with a zero potential is formally identical to the heat equation in the sense that we just make ...
user28109
1
vote
1
answer
99
views
Should the derivative of an array be calculated array by array or element by element in CFD codes?
I am making my own finite difference computational magnetohydrodynamic code in Fortran 90. Looking at other codes they appear to calculate for example their $x$-derivatives, bb of their variables, e.g....
- 219
0
votes
0
answers
229
views
Double mach reflection at a inclined wedge
I am running into a strange problem when solving the 2D compressible Euler equations on a inclined wedge. To elaborate, my top boundary condition seems to emitting some type of instability. I have ...
- 75