# 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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### How to avoid density getting “deleted” in two way rigid body coupling with LBM CFD?

I've been reading this paper recently, which talks about using Lattice Boltzmann methods and two way coupling. Specifically, it outlines fluid solid coupling, and solid fluid coupling, and how simply ...
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### What precautions should be taken when using 2D Perfectly Matched Layers?

I'm solving linearized Navier-Stokes equations with Perfectly Matched Layers in two spatial directions $x$ and $y$, but in the time-harmonic frequency $\omega$-domain, which is meant to be less ...
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### Derive the Finite Difference equation corresponding to the steady state PDE. Explain how to implement Dirichlet and Neumann boundary conditions

A rod of length L = 1m, is made of copper, with thermal conductivity κ = 380W/m/K. A uniform heat supply h = 10kW/m3 is applied to the rod. The left boundary of the rod is kept at constant temperature ...
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### DirichletBC definition on boundary subdomain for component of vector valued function in FEniCS

I am trying to impose a no-outflow condition for a velocity-field over a boundary sub-boundary domain in FEniCS. What I have find challenging is imposing the condition on a component of a vector-...
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### Is the diffusion equation with Neumann and Dirichlet BCs well-posed?

I am considering the following diffusion equation: $$\frac{\partial f}{\partial t} = \frac{\partial}{\partial x}[D(x,t)\frac{\partial f}{\partial x}]$$ over a grid ...
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### CFD and finite volume method: Dirichlet boundary conditions for the Euler equations

Please point me to an answer if one already exists, but after some searching, I still can't find the answer to what seems like a very simple question. There are plenty of references out there for ...
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### Solving a system of PDEs with no-flux boundary conditions (finite difference discretization)

I am interested in solving a system of linear PDEs with the finite difference method and I'm having trouble to solve the no-flux boundary condition correctly. \begin{align} \frac{\partial n}{\partial ...
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### Interpreting results of using no-flux boundary condition

I am solving for solute transport in 1 D. $$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\partial C}{\partial x}$$ No-flux boundary condition is imposed at both the ...
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### Implementing structured grid boundary conditions using NumPy arrays?

I am making a toy code in Python to solve the advection equation $$u_t + cu_x = 0$$ with, for example, periodic boundary conditions. Background information The numerical grid is specified like this: ...
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### How to implement the following Finite Element method for Burgers' equation?

I am trying to replicate this result. It involves using the Galerkin finite element approach onto the viscous Burgers' equation. However, my implementation (in R) seems to be giving me wrong results....
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### Well-posedness of Navier-Stokes equation

Before running a simulation for turbulence (e.g Rayleigh-Benard Convection), how do we check for well-posedness of Navier-Stokes with other equations for a given boundary condition?? Can someone ...
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### Implementation of boundary conditions for 1D Euler equations

I'm trying to solve 1D Euler equations with gravity in spherical coordinates using a finite-difference TVD MacCormack method on a non-uniform grid of $N$ components, following the method provided in ...
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### Linear elasticity modeling load using traction vs. mixed BC

In classical linear elasticity, when modeling a force/load boundary condition, it appears that we could either: Use a pure Neumann boundary condition, where the 3 traction components are specified. ...
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### Harmonic oscillators with periodic boundary conditions

I am trying to simulate multiple harmonic oscillators in periodic boundary conditions (subsequently visualizing the process in VMD). I have successfully simulated multiple HOs by using the Leapfrog ...
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### Structural boundary conditions - rotational/translational DoFs and displacement/tractions BCs

I am a little bit confused over the concept of translational and rotational degrees of freedom (DoFs) in structures, and their relation to displacement/traction BCs. Do displacement boundary ...
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### Non linear Parametric BVP with inequalities

Consider a non linear ode in dimension $10$: $\dot x = f(t,x,\lambda)$ where $\lambda$ is a vector of $p$ parameters. Consider a boundary value problem of the form : $\dot x(t) = f(t,x(t),\lambda)$ ...
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### Combining multiple coupled 1st order equations in python

I'm having serious troubles with solving translating 3 coupled differential equations into python. The 3 DE's stem from a 4th order DE used to calculate the bending moment of an underwater pipeline ...
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### Interatomic distance-periodic boundary conditions-non cubic unit cell

I am trying to find interatomic distance considering periodic boundary conditions for hexagon cubic cells (graphite). I tried to follow the answers to these two questions here but am unable to get the ...