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### Strange oscillation when solving the advection equation by finite-difference with fully closed Neumann boundary conditions (reflection at boundaries)

I am trying to solving the advection equation but have a strange oscillation appearing in the solution when the wave reflects from the boundaries. If anybody has seen this artefact before I would be ...
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My long-term goal is to numerically solve the 1D advection-diffusion equation of the form: $$\frac{\partial u}{\partial t}=\frac{\partial }{\partial x}\left( v(x,t) u+D\frac{\partial u}{\partial x}\... 1answer 2k views ### Trouble implementing Neumann boundary conditions because the ghost points cannot be eliminated Neumann boundary conditions are implemented by introducing ghost points outside the domain and then using the boundary conditions to eliminate the ghost points. For example, see this question. I ... 3answers 2k views ### No flux boundaries for mixed hyperbolic parabolic PDE I read this post, "Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation" and although it is the same type of equation it does not fit ... 1answer 646 views ### Conservative finite-difference expression for the advection equation Following on from the earlier question I am trying to derive a finite-difference scheme for the advection equation which is conservative. It was suggested that for advection equation with variable ... 1answer 1k views ### Implementation of gradient zero boundary conditon in advection-diffusion equation My question is about Finite Element Method. I want to know how to implement "gradient zero" conditions to advection-diffusion equations in conservative form like, \frac{\partial \rho}{\partial t} + ... 1answer 391 views ### Implementing Robin Boundary condition (finite difference) I'm interested in applying Robin boundary condition to a convection-diffusion problem in 1D. In the following system,$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\...
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 (...