# 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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### Wave equation, wave is bouncing off Neuman boundary

Wave equation. Mixed BC. Applied Neuman boundary condition ($\frac{\partial u}{\partial x}\big|_N=0$) to the RHS of the domain You may observe the sharp edge in the middle of the string in the image ...
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### Non-reflective boundary condition

I'm currently solving incompressible Navier-Stokes system of equations with periodic flow and high viscosity. Is there any outlet boundary types that avoids the reflection of flow from the outlet back ...
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### deal.ii - ParaView "warp by scalar" of my output is not continuous

During our finite element course, we've solved the linear elasticity problem in 2D on a square (GridGenerator::hyper_cube) with $Q_1$ bilinear finite elements in ...
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### Displacement field not correct?

Consider the elastic equation $$- \operatorname{div}(C \nabla \mathbf{u}) = \mathbf{f}$$ as presented in step-8. Here $\mathbf{u}$ is the displacement vector, let's consider the 2d case. As you can ...
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I am currently attempting to use FEnICS to solve an electrostatic problem with two materials of different permittivity $\varepsilon_1$ and $\varepsilon_2$ forming an interface: Consider a domain $\... • 43 1 vote 0 answers 63 views ### Constrained optimization for non-linear equations in octaveGNU I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ... 1 vote 0 answers 125 views ### Weak form of Elliptic problem with mixed Dirichlet & Neumann conditions Let$\Omega \subset \mathbb{R}$in a bounded polygon domain and$f:\Omega \to \mathbb{R}$known function.We split the boundary into two parts$\partial \Omega_{1}$and$\partial \Omega_{2}$such that$... 36 views

### Insert a boundary condition without removing periodicity assumption

I've to perform a multi-fluid internal flow simulation with a code which intrinsically assumes periodicity on a given direction (say z) on a cartesian grid. Nonetheless, the problem I'm trying to ...
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### How to solve second order coupled non linear differential equations

For a project I am doing, I have to solve the following system of differential equations numerically using my own code: $$x^2K'' = KH^2 + K(K^2-1)$$ and, $$x^2H'' = 2K^2H + \alpha H(H^2-x^2)$$ ...
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I am trying to model a 1-d advection-convection numerically, using an upwind scheme. I'm using the following equation to calculate the value of internal cells: $$C_x^{t+1} = C_x^{t} + D\frac{\Delta t}{... • 119 0 votes 0 answers 114 views ### Boundary conditions for an FEM approximation of the Laplace operator Using FEM, I want to approximate the Laplacian$$u = \nabla \cdot \nabla h \, ,$$where h(x,y) is an FEM approximated scalar field on the same mesh, i.e. piecewise differentiable. I am using MOOSE ... 2 votes 0 answers 30 views ### Semi-analytical/empirical modelling of wall boundary conditions in advection-diffusion-reaction equation with distributed source Let's suppose I need to numerically solve a 3D steady-state transport equation of the form$$ \nabla \cdot (\mathbf{u} c) = \nabla \cdot (D \nabla c) - \lambda c + S where c is the transported ... • 21 1 vote 0 answers 79 views ### Solving Laplace equation with constraint on boundary I have found the following PDE problem in a paper: Essentially, we have a rectangular domain where there is a unknown interface z=\xi(x) (liquid-air interface) separating the domain into two medium ... • 217 2 votes 0 answers 251 views ### How are finite volume method boundary conditions implemented without using ghost-cells? I'm currently trying to implement my own FVM code in cpp, but when I try to calculate the laplacian of a test function, given by \begin{align}\phi_0=\sin(2\pi x)\sin(2\pi y),\end{align} I get ... • 21 0 votes 0 answers 279 views ### Poisson equation, stiffness matrix positive definiteness, Dirichlet boundary conditions I have a question regarding the positive definiteness of the stiffness matrix. Specifically, I believe that it should be positive definite only when at least one Dirichlet point is given, so I would ... • 429 2 votes 0 answers 53 views ### How to solve this boundary value problem which has more unknown than equation on MATLAB I need your helps about solving the problem below with MATLAB. I am trying to solve 2D Stress Wave Propagation problem by using FDTD(Finite difference time domain) method on the cylindrical coord. I ... 0 votes 0 answers 50 views ### Cauchy problem ill-posed? Find the solution to the Cauchy problem consisting of the wave equation :u_{xx}-u_{yy}=0$$together with initial conditions:$$ u(x,0)=0,u_{y}(x,0)=g(x) for some known initial datum $g$. Is ... 