# 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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### Numerical implementation of the Dirichlet-to-Neumann map

I am solving the Dirichlet problem $$\begin{cases} \Delta u = 0, \\ u|_{\partial D} = f, \end{cases}$$ in a $2d$ domain $D$ using the finite element method. What I want to get is the ...
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### A Question About a Claim from 1991 Computational EM paper about the Cancellation of certain Boundary Terms

Please let me know if this is not the appropriate site for this question. I found questions regarding EFIE/MFIE/CFIE on this site, so I thought my question might fit. I am studying the paper by Putnam ...
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### Understanding Boundary Condition in FEM

I am trying to understand Dirichlet and Neumann boundary conditions in FEM and I wanted to know if my inference is correct. To articulate my understanding, lets consider a simple case of TE and TM ...
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### Do practice and theory differ substantially when implementing Neumann Boundary Conditions using a Mixed Method?

I have implemented a pretty straightforward finite element solver for the following Poisson equation. For the purposes of this question we can assume the source term and the Dirichlet data both ...
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### Boundary conditions in the Finite Element Method at only one side of computational domain

I want to solve a Sturm-Liouville problem in 1D, i.e., \begin{align} [p(x)\ u'(x)]'+q(x)u(x) = f(x) \end{align} with boundary conditions \begin{align} u(0)=a \hspace{1cm} u'(0)=b \end{align} How do I ...
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### Non-reflecting boundary conditions for compressible Navier-Stokes equations

I have some questions about the implementation of non-reflecting OUTFLOW boundary condition for Navier Stokes equations. Following Poinsot, Lele "Boundary Conditions for Direct Simulations of ...
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### Neumann-Neumann boundary intersection

I am trying to solve a Vertex Centered, Finite Difference, Poisson equation $-\nabla^{2}u=f$ with Dirichlet boundaries on the left and bottom and Neumann boundaries on the top and right using ...
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### Transport Equation in a Tube: Source Term on Boundary

I'm modeling mass transport in a flow reactor. The flow reactor is a tube, which allows me to use cylindrical symmetry in solving the Convection-Diffusion-Reaction (CDR) Equation, which governs the ...
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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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### 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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### Advection diffusion equation using Crank-Nicolson with total flux and Diriclet BCs

I am trying to model the 1D advection-diffusion equation: $${\partial c \over \partial t} = D_c{\partial^2 c \over \partial x^2} -u{\partial c \over \partial x}.$$ With Robin boundary conditions that ...