# 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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### Symmetry axis boundary condition

I was wondering about the symmetry axis boundary condition in commercial CFD solvers such as ANSYS Fluent. If the problem is the flow through a round pipe or out of a round nozzle, it is natural to ...
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### Solving Poisson's Equation with Periodic Boundary Conditions

So, I've been attempting to design a simple solver for a problem of finding the gravitational potential of a system using Poisson's equation (let's call the potential phi, $\phi$). The goal is that I ...
1 vote
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### Crank Nicolson Method with closed boundary conditions

I want to simulate 1D diffusion with a constant diffusion coefficient using the Crank-Nicolson method. $$\frac{\partial u (x,t)}{\partial t} = D \frac{\partial^2 u(x,t)}{\partial x^2}.$$ I take an ...
1 vote
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### How can we use the two boundary conditions for the Taylor-Maccoll Equations for Cone Shock Waves?

The Taylor-Maccoll equations below govern the gas dynamics around a supersonic, axially oriented cone. Using the notation from Anderson's Fundamentals of Aerodynamics, which uses a dimensionless ...
1 vote
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### Why do we use modified pressure in incompressible multiphase solvers with gravity?

The context of my question is two-phase incompressible solvers such as interFoam in OpenFOAM, but I have seen this trick used ...
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### Why is the maximum potential energy greater than the maximum kinetic energy?

I was plotting the energy variation in a mass-spring system. If I define the initial conditions to be at maximum displacement from the origin, the potential energy is plotted correctly but kinetic ...
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### Analytical Equation of the gaussian 1D wave equation with periodic Boundary condition

I am trying to validate the 1D analytical wave equation with a numerical solution with periodic boundary conditions. I have implemented the periodic boundary condition for the numerically calculated ...
1 vote
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### How to include zero flux boundary conditions?

I am trying to solve the following differential equation in the domain of $\theta \in [0, 2 \pi]$ using finite differences scheme: For $0< \theta \leq \pi$ \begin{align} \rho_i^{n+1}=\rho_i^{n}+D\...
1 vote
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### Boundary value problem solver fails on trivial case

I am trying to solve a boundary value problem on $[0, \infty]$, using scipy's scipy.integrate.solve_bvp and I am seeing that the solutions are not converging even ...
164 views

### Can successive over-relaxation (SOR) method deal with ill-posed PDE BVP?

Recently, I've been struggling to understand the limitations and capabilities of the successive over-relaxation (SOR) method for boundary value problems which are ill-posed, such as, for instance, ...
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### How to Impose nonhomogeneous Neumann Boundary Condition in the DG Formulation

Consider the following partial differential equation \begin{align} \frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\ u(x,0) &= u_{0}(x) ...
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### DG method for solving Hyperbolic Partial Differential Equation with Dirichlet Boundary Conditions

Consider the following partial differential equation \begin{align} \frac{\partial u}{\partial t}+\frac{\partial f}{\partial x} &= g(x,t), \ \ x\in \Omega = [x_{L},x_{R}] \\ u(x,0) &= u_{0}(x) ...
1 vote
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### An explanation of 2delta waves on non-staggered grids

While looking into the difference between staggered and collocated grids, I came across an effect called $2\Delta x$-oscillations, which happen on non-staggered grids, but not on staggered grids. This ...