# 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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### Pressure boundary condition in Navier-Stokes equations

I would like to solve 3D transient incompressible Navier-Stokes with FEM, Newton method, Schur-based preconditioner, Lagrangean P2/P1 elements (no stabilization), in a rigid pipe discretized with ...
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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 ...
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### Closed boundary conditions in finite difference method for diffusive-advective equation

I am implementing a finite difference method in solving the diffusive-advective equation: $$u_t + v \cdot u_x = D\cdot u_{xx}$$ (v, D are constants). Planning to use the operator splitting method (...
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### Moving airfoil boundary conditions

I am trying to simulate a moving airfoil with constant speed (Mach=0.755, aoa=1.25). I solve Euler equations with Roe's method. I have two boundary conditions: Farfield Slip wall (airfoil) For all ...
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### Boundary conditions for second order PDE

For a second order PDE, for example heat conduction equation $\frac{\partial T}{\partial t} = \frac{\alpha}{C_p} \nabla^2 T$, is it possible to determine the steady-state (or even transient) solution ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Residual of Poisson equation with periodic boundaries

I am trying to write a multigrid solver for Poisson's equation, $-\Delta u=f$, on the unit square, $\Omega=(0,1)^2$ with periodic boundaries. My primary source has been Multigrid by Trottenberg, ...
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### How to account for a corner node with zero-flux condition at an extrapolated distance

I am trying to implement a numerical solver and am having troubles dealing with boundary conditions, especially in the corners. I have a 2D mesh, and on the left I have a Dirichlet condition, on the ...
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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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### 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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### FEniCS: both normal and shear stress boundary conditions for elasticity? [closed]

I would like to have both the normal (xx) component and shear (xy) component of a 2D (stress) tensor defined on a boundary (y=const, for instance) for an equation which is of the type  \nabla \cdot ...
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### Implementation of no-slip boundary conditions in lattice Boltzmann method fluid simulation

My faculty advisor recommended that I take a look at the lattice Boltzmann method as an introduction to scientific computing and potentially an undergraduate honors thesis topic. I cooked up a some ...
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### Arbitrary Choosing of the Solution Domain - Navier Stokes and Manufactured Solutions

I want to verify a finite-volume solver (SIMPLE-Algorithm) for the incompressible Navier-Stokes equations by using a manufactured solution. I use Dirichlet boundary conditions for the velocity at all ...
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### Treatment of Neumann (Traction) boundary conditions using projection methods

I am looking to solve the incompressible Navier-Stokes equations in 3D, using an inflow boundary condition specifying a velocity: $\mathbf{u} = \mathbf{g}_0 \,\, \forall \,\, \mathbf{x} \in \Gamma_u$ ...
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### boundary conditions with non-constant coefficients in cell centred finite volume method

Suppose am solving the heat conduction equation in 1d with Dirichlet boundary conditions. The thermal conductivity $k$ is a non constant function. So $-(k(x)u'(x))' = f(x)$ The value of $k$ enters the ...
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### Finite Difference for Hamilton Jacobi Belman

I have hjb equation where $V=V(x,t)$ and $u=u(x,t)$ $V_t + \sup(u) [A(x,u)V_x + B(x,u)V_{xx}]=0$ for $x$ in $[0,1]$ and $t$ in $[0,1]$ I have been able to successfuly resolve it numerically having ...
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### Newton Iteration method convergence

I wrote a Python code which solves a second degree nonlinear differential equation using the Newton iteration method. The code converges to a 2-cycle within 50 or so iterations. The cycle only ...
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### Boundary condition for Pressure in Navier-Stokes equation

I am reading the paper, http://math.mit.edu/~gs/cse/codes/mit18086_navierstokes.pdf I could not really understand the description. Could someone explain a little bit more? It says, "For the lid ...
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### inclined/general Dirichlet boundary conditions

For simpilcity, consider a single quad linear elasticity finite element in 2D. The Dirichlet boundary conditions on node 1 and node 2 are easy to implement and can be handled in the standard way. ...
I have a PDE defined over $\mathbb{R}$, for which I don't have the exact solution, and I am to approximate it with finite differences so I need to input some BC. Can anyone suggest any good ...