For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.
1
vote
1answer
41 views
FEniCS: how to specify boundary conditions on a circle inside 2D mesh
I would like to numerically find a mutual capacitance of two stripes of metal on the opposites sides of a cylinder. The problem is obviously a 2D Laplace equation. I would like to find the potential ...
1
vote
1answer
29 views
CFD (Fluent) define a inlet for a tidal basin
I'm still pretty new in the CFD modelling world.
Can anyone advise me how to define a inlet for a tidal basin in Fluent?
The water level and the velocity at the inlet vary in time due to the tide ...
3
votes
1answer
59 views
Trouble implementing Neumann boundary conditions because the ghost points cannot be eliminated
Neumann boundary conditions are implemented by introducing ghost points outside the domain and then using the boundary conditions to eliminate the ghost points. For example, see this question.
I ...
3
votes
1answer
109 views
FEniCS: separate boundary conditions in normal and tangential direction of mesh boundary
Given a vector-valued PDE, I'd like to enforce the boundary conditions
$$
\vec{n}\cdot u = g\\
\vec{n}\cdot \nabla (\vec{t}\cdot u) = 0
$$
on the solution $\vec{u}$. If the boundary happens to align ...
5
votes
1answer
85 views
Example of a PDE model with nonlinear Dirichlet boundary conditions
Is there any application for PDEs with nonlinear Dirichlet boundary conditions? That is, I am looking for an example of a partial differential equation for a state $u$ posed on a domain $\Omega$ with ...
2
votes
0answers
135 views
Newton Iteration method convergence
I wrote a Python code which solves a second degree nonlinear differential equation using the Newton iteration method. The code converges to a 2-cycle within 50 or so iterations. The cycle only ...
2
votes
1answer
114 views
Role of boundary conditions (e.g. periodic) in Poisson equation
Given 3D Poisson equation
$$
\nabla^2 \phi(x, y, z) = f(x, y, z)
$$
and the right hand side and the domain, am I free to impose any boundary conditions (BC) on the function $\phi$, or do they have to ...
4
votes
2answers
133 views
No flux boundaries for mixed hyperbolic parabolic PDE
I read this post, "Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation" and although it is the same type of equation it does not fit ...
2
votes
3answers
111 views
Open boundary conditions with the advection-diffusion equation
Following on from my previous equation I'm would like to apply open boundary condition to the advection-diffusion equation (with reaction term),
$$ \frac{\partial \phi}{\partial t} = ...
7
votes
1answer
171 views
Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation
I don't understand the different behaviour of the advection-diffusion equation when I apply different boundary conditions. My motivation is the simulation of a real physical quantity (particle ...
0
votes
0answers
69 views
Marker and Cell Method (MAC) - STOKES FLOW - boundaries?
please can you help me with my problem with Stokes flow written using Marker and cell method (MAC)? I need only to solve the eq. of continuity + momentum eq. for a given condition (steady state). I ...
4
votes
1answer
116 views
mathematical statement of “open” boundary condition
For your information, the original equation comes from here. Note: You DON'T have to read the paper. I will make the question as self-contained as possible.
The central equation to solve is equation ...
5
votes
2answers
540 views
Writing the Poisson equation finite-difference matrix with Neumann boundary conditions
I am interested in solving the Poisson equation using the finite-difference approach. I would like to better understand how to write the matrix equation with Neumann boundary conditions. Would someone ...
5
votes
3answers
103 views
which numerical method for ode with mixed BCs
I've got a second order nonlinear ODE (nothing fancy), but the BC are a little odd to me:
$y'(0) = 0$
$y \rightarrow y_a$ as $x \rightarrow \infty$
What's a good numerical method for solving ...
5
votes
1answer
276 views
How to properly apply non-homogeneous Dirichlet boundary conditions with FEM?
In general, Dirichlet boundary conditions won't be satisfied exactly for FEM for non-homogeneous boundary conditions. The FEM codes I've seen set the degrees of freedom to interpolate the Dirichlet ...
5
votes
1answer
71 views
how to visualize lattice with periodic, helical, etc. boundary conditions?
I am trying to write a special hexagonal lattice generator, with several kinds of boundary conditions, such as helical BC, periodic BC, and I find it hard to verify whether it works correctly. I tried ...
4
votes
1answer
103 views
How do I solve an ODE Two-Point Boundary Value Problem?
I have a feeling my question is a very basic one, but I am not at all well versed in computational sciences.
My equations are of the form:
$$
y \in \mathbb{R}^3 \\
\dot{y}(t) = f(y(t)) \\
y_1(0) = a ...
4
votes
1answer
86 views
Neumann BCs in cylindrical geometry (FEM)
I was wondering where I could get a detailed account (either in print or online) on applying a Neumann/mixed Boundary condition along the $r=0$ axis in an axially symmetric geometry. Though this is a ...
3
votes
4answers
498 views
Heat equation (steady state) with boundary conditions at domain edges and inside the domain
I'm trying to solve the steady state of a heat equation problem in 2D $\Delta u = 0$ (3D also), with the method of solving the huge system of equations that arises from the discretization of the ...
5
votes
1answer
185 views
Mixed boundary conditions Finite Element Method
I have the following problem in Finite Element Method
$$ -(\alpha u')' + \beta u' + \gamma u = f$$
with $ \Omega = (0, 1)$, $ u(0) = 0 $ and $ u'(1) = 3 $
to be able to write the weak formulation ...
7
votes
3answers
430 views
Boundary conditions for the advection equation discretized by a finite difference method
I am trying to find some resources to help explain how to choose boundary conditions when using finite difference methods to solve PDEs.
The books and notes which I currently have access to all say ...
8
votes
4answers
934 views
solving coupled ODEs with initial-value and final-value constraints
The essence of my question is the following: I have a system of two ODEs. One has an initial-value constraint and the other has a final-value constraint. This can be thought of as a single system with ...
3
votes
2answers
187 views
What numerical methods are recommendable for simulating two phase immiscible fluid flow through a pipe with high capillary pressure?
I'm simulating two phase immiscible drainage (air displacing water) in a rectangular domain of size .6mm x 2.4mm (2 dimensions) using Ansys FLUENT software. I am using an implicit Volume of Fluid ...
11
votes
3answers
276 views
How to incorporate the boundary conditions with the Galerkin method?
I've been reading some resources on the web about Galerkin methods to solve PDEs, but I'm not clear about something. The following is my own account of what I have understood.
Consider the following ...
6
votes
1answer
151 views
Adaptive mesh refinement with perfectly matched layers?
We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...
5
votes
1answer
417 views
Schrodinger equation with periodic boundary conditions
I have a couple of questions regarding the following:
I am trying to solve the Schrodinger equation in 1D using the crank nicolson discretization followed by inverting the resulting tridiagonal ...
7
votes
1answer
234 views
Which fourier series is needed to solve a 2D poisson problem with mixed boundary conditions using Fast Fourier Transform?
I have heard that a fast fourier transform can be used to solve the poisson problem when the boundary conditions are all one type... Sine series for dirichlet, cosine for neumann, and both for ...
