# 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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### What Linear Equation Solver should be used for a problem with many dirichlet conditions?

I am solving a laplace equation on a finite-element mesh (tetrahedral, triagonal) and have many say 99% dirichlet conditions compared to the number of unknowns. Is there an efficient way to solve this ...
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### 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 ...
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### Applying Dirichlet b.c. to the Eigenvalue-Problem

If you use a FEM (on the variational formulation), you can discretize some continuous eigenvalue problem, $$L u = \lambda u \ \ \text{on} \ \Omega,$$ into some discrete, generalized eigenvalue problem,...
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### Best practice for dealing with Dirichlet boundary conditions in finite-difference schemes: add artificial unknowns?

I know of at least two ways of dealing with Dirichlet boundary conditions in finite-difference schemes (and, to a lesser extent, finite-element schemes). Here I'm thinking of solving Poisson's ...
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### periodic boundary conditions for triclinic box

I am trying to do analysis on a data set of atomic coordinates generated form lammps. I simulated an alpha glycine crystal in a triclinic box. The box vectors look like the following, where xy,xz,and ...
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### 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 ...
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### Recovering pressure from velocity or streamfunction fields

I am interested in 2D channel flow of an incompressible Stokes fluid (Re << 1), with periodic boundary conditions in the x-direction and no-slip at the walls in the y-direction. I have existing ...
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### Finite Difference Method Neumann Boundary Condition with Variable Coefficients

Disclaimer In the process of typing up this question, I determine its solution. Since I went through the trouble of typing up the question in its entirety, I will post its answer as well. It may ...
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### How can i convert a boundary flux condition into an internal source term?

Imagine a rectangular box that is thermally insulated on all sides except for one, where a heat flux is applied. Now imagine the same box with the same conditions on all sides except that the side ...
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### Interface Formulation at Finite Volume Boundaries when using the Dual Mesh

When using the dual mesh (vertex-centered) for finite volume methods, you end up with a cell center at the boundaries between materials. It is possible that the equations being solved in each ...
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### Numerical solution of zero-potential time-dependent Schrödinger equation in 1D

I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$ My issue is that I don't have the physical background to understand ...
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### 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 (...
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### How to implement boundary conditions on Finite Difference WENO5 scheme for the Euler equations

I'm implementing a Finite Difference WENO5 with Lax-Friedrich flux splitting on a uniform, structured grid to solve the 2D Euler equations of fluid dynamics on a rectangular domain in cartesian ...
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