Questions tagged [boundary-conditions]
For questions regarding the choice and/or appropriateness of conditions necessary to model a particular phenomenon with a partial differential equations.
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Boundary Conditions on the Inlet and Outlet in a Discontinuous Galerkin framework
In the book Discontinuous Galerkin Method (DGM), Analysis and Applications to Compressible Flow by Vít Dolejší and Miloslav Feistauer, Springer, it is mentionned, in section 8.3.2 that deals with ...
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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 ...
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Imposing higher order finite difference schemes for boundary value problems on a finite interval
I have some questions. I'm going to assume everything is in 1d with a Laplacian operator. If I discretize the Laplacian operator using $p = 2a+1$ grid points with periodic boundary conditions, I ...
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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), \...
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Galerkin Method - Why does integration-by-parts eliminate need to enforce Neumann boundaries?
I've posted this to MathStackexchange but I figured I'd also post here as well as I have yet to receive an answer on my original post, and that I would be more likely to encounter users of the ...
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Are there necessary conditions for SOR algorithm to converge when used for 2D discrete Poisson problem, with PBC, besides solvability condition?
I am trying to solve a 2D poisson problem that is supposed to represent diffusion of chemicals on a grid: $\nabla^2 R_{ij}=f_{ij}$. I am discretizing the problem with the standard central ...
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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 ...
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How to handle non bilinear weak form?
I solved the 2D heat equation using the finite element method. It all went well first with the adiabatic case, however problems occured when I introduced cooling with the enviroment.
I modeled the ...
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How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary
Problem
I am using finite difference method to solve classic problem of flow around cylinder, for validation of my group's immersive boundary method.
The common way to validate numerical method is ...
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finite difference method not working when going to two dimensions
I have two coupled ordinary differential equations in the steady state:
The following code solves, using the Jacobi finite difference method, in 1d using Dirichlet boundary conditions for function $...
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How to correctly implement boundary conditions with Chebyshev differentiation matrix?
In my code I am able to implement zero Dirichlet boundary conditions, however, in my opinion my method does not seem to be as smooth and effective as possible. I am solving a Poisson's equation with ...
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How to impose boundary conditions when solving a nonlinear dynamical system given by the FEM solver
I am solving a nonlinear dynamical system given by a nonlinear elastic problem which takes the following form:
$$ \boldsymbol{M} \ddot{u} + \boldsymbol{K}_{\textrm{NL}}u = 0 ,$$
here $u \in \mathbb{R}...
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How to evaluate the points near/at the boundary when using Richardson extrapolation for improved accuracy of a derivative
If we want to improve the accuracy of our numerical estimation of a derivative, we can use Richardson extrapolation. The method is very beneficial when using a centered difference scheme and the ...
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What is the correct way to implement Neumann type boundary conditions for solving a PDE using Chebyshev's collocation method?
I am studying spectral methods for solving PDEs numerically. I finished a chapter that explains how to use Chebyshev's collocation method to solve them. Though the explanation in the book is quite ...
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Non-standard boundary condition for incompressible Navier Stokes
I am having difficulties applying the boundary condition
$$\frac{\partial \vec{V}}{\partial t} + u\frac{\partial \vec{V}}{\partial x} = \frac{1}{\operatorname{Re}}\frac{\partial ^2 \vec{V}}{\partial y^...
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