All Questions
Tagged with pde boundary-conditions
92
questions
1
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0
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42
views
How can I apply a mixed boundary condition to a multi-material heat transfer problem using Crank-Nicolson?
I am working on a mixed material model for a melting material and need to enforce both a Dirichlet and Neumann type condition at the interface. Subject to an external surface heat flux at the top of ...
- 11
1
vote
1
answer
53
views
How to obtain the transfer function between boundary condition and point of wave equation?
I am considering the wave equation with position varying material properties
$$
m(x) \frac{\partial^2 u}{\partial t^2} = \frac{\partial}{\partial x}\left(k(x) \frac{\partial u}{\partial x}\right), \...
- 470
1
vote
1
answer
104
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Boundary conditions of a 2D explosion case
I want to solve this problem explosion test case. I was wondering about what are usual the boundary conditions for this type of problems. I want the wave to bounce of the boundary of the domain (let's ...
- 147
0
votes
0
answers
64
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How to set Neumann BC for coupled transport problem in weak form?
Consider
$$\begin{aligned}
\partial_t v + b\cdot \nabla \phi &=0 \\
\partial_t \phi + b\cdot \nabla v &= 0
\end{aligned}$$
for $v:(x,y)\mapsto \mathbb{R}$, unknown and time-dependent ($...
2
votes
1
answer
99
views
Symmetrization of Laplacian Matrix Operator (finite volumes)
The aim is to construct symmetric Laplacian matrix $L$ for 2D square domain.
I have the following discretization of second derivatives on non-uniform grid (will skip the steps of derivation, any ...
- 362
1
vote
1
answer
52
views
Applying spectral method to a damped, driven 2D bending-mode wave equation on an irregular domain with heterogeneous boundary conditions
I'm trying to model some two-dimensional waves, and am unsure how to combine my boundary conditions with spectral methods. The PDE I'd like to explore resembles the equations for damped, driven ...
- 153
0
votes
1
answer
220
views
Can successive over-relaxation (SOR) method deal with ill-posed PDE BVP?
Recently, I've been struggling to understand the limitations and capabilities of the successive over-relaxation (SOR) method for boundary value problems which are ill-posed, such as, for instance, ...
- 83
1
vote
1
answer
301
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Convergence stall when solving 2D Poisson PDE with pure Neumann boundaries (finite differences)
I recently started coding a small library of 2D PDE solvers (time dependent and time independent), and my first attempt was a 2D Poisson equation of the form:
$$\nabla(\epsilon\nabla\varphi)=\nabla\...
- 83
0
votes
2
answers
481
views
Solving a generalized eigenvalue problem with Chebyshev spectral method: How to impose boundary conditions into the matrices?
I'm solving a local instability problem for a pipe Poiseuille flow.
The coordinate system is columnar, i.e., ($r,\theta,x$) (radial, tangential and axial).
The basic flow is $\bar{u_r}=0, \bar{u_\...
- 1
2
votes
3
answers
153
views
Simple to program method for elliptic PDE with curved boundary?
I know very little about numerical PDE, so I apologize if this equation is ill-formed (and I appreciate any corrections).
I am currently learning about Brownian motion. A classic result is that we can ...
- 105
0
votes
0
answers
89
views
Transparent Boundary Conditions for Finite Difference ADI PR 2D TDSE solution
I want to put (non-dirichlet) boundary conditions inside the code I wrote to solve the 2dim TDSE using the alternating direction implicit Peaceman - Rachford method.
$$
(1 + iB\Delta t/2 ) \psi^{n+1/2}...
- 141
3
votes
0
answers
70
views
Change in Variables applied to biharmonic equation
Background
I want to solve the following biharmonic equation:
$$\frac{ \partial^4 s }{ {\partial \xi}^4 }+\frac{ \partial^4 s }{ {\partial \xi}^2{\partial t}^2 }+\frac{ \partial^4 s }{ {\partial t}^4 }...
- 31
1
vote
1
answer
100
views
How to Impose nonhomogeneous Neumann Boundary Condition in the DG Formulation
Consider the following partial differential equation
\begin{align}
\frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\
u(x,0) &= u_{0}(x) ...
- 83
3
votes
0
answers
54
views
Appropiate Artificial Boundary Conditions for the radial part of the Klein Gordon equation?
I am trying to simulate the following equation using FDTD
$ \left(- \partial^2_t + \partial^2_x + V(x) \right) \psi(x,t) =0 $
subjected to the initial conditions $\psi(x,0) = f(x),~ \partial_t \psi(x,...
- 131
0
votes
1
answer
1k
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1D wave equation using Finite difference method MATLAB
I have the wave equation
$$u_{tt} = 4 u_{xx}$$
with the boundary conditions
$$u(0,t) = u(L,t) = 0\,,\quad x \leq 0 \leq 2\pi \,,\quad t\geq 0$$
and initial conditions
$$\begin{align}
&u(x,0)=\...
