# 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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### 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 ...
1answer
617 views

### Problem in Discretizing Convection-Diffusion-Reaction equation

I'm trying to solve the Convection-Diffusion-Reaction (CDR) equation on a rectangular domain, using cylindrical coordinates and Finite Difference Methods (FDM) (this approximates a flow reactor). ...
1answer
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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 ...
3answers
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### Role of boundary conditions (e.g. periodic) in Poisson equation

Given 3D Poisson equation $$\nabla^2 \phi(x, y, z) = f(x, y, z)$$ and the right hand side and the domain, am I free to impose any boundary conditions (BC) on the function $\phi$, or do they have to ...
3answers
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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 ...
3answers
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1answer
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### Neumann BCs in cylindrical geometry (FEM)

I was wondering where I could get a detailed account (either in print or online) on applying a Neumann/mixed Boundary condition along the $r=0$ axis in an axially symmetric geometry. Though this is a ...
4answers
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### Heat equation (steady state) with boundary conditions at domain edges and inside the domain

I'm trying to solve the steady state of a heat equation problem in 2D $\Delta u = 0$ (3D also), with the method of solving the huge system of equations that arises from the discretization of the ...
1answer
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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 ...
4answers
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### Boundary conditions for the advection equation discretized by a finite difference method

I am trying to find some resources to help explain how to choose boundary conditions when using finite difference methods to solve PDEs. The books and notes which I currently have access to all say ...
4answers
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### solving coupled ODEs with initial-value and final-value constraints

The essence of my question is the following: I have a system of two ODEs. One has an initial-value constraint and the other has a final-value constraint. This can be thought of as a single system with ...
2answers
429 views

### What numerical methods are recommendable for simulating two phase immiscible fluid flow through a pipe with high capillary pressure?

I'm simulating two phase immiscible drainage (air displacing water) in a rectangular domain of size .6mm x 2.4mm (2 dimensions) using Ansys FLUENT software. I am using an implicit Volume of Fluid ...
4answers
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### How to incorporate the boundary conditions with the Galerkin method?

I've been reading some resources on the web about Galerkin methods to solve PDEs, but I'm not clear about something. The following is my own account of what I have understood. Consider the following ...
1answer
270 views

### Adaptive mesh refinement with perfectly matched layers?

We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...