Questions related to solving the advection-diffusion equation using numerical methods, including derivation and implementation of boundary conditions.

74 questions
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### How to solve coupled steady laminar diffusion flame jet problem? [closed]

I am trying to solve governing equations of laminar diffusion flame jet for steady state case. In the next step, I will solve for unsteady case. I have non-dimensional continuity, axial momentum, ...
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Would you know what is the condition for stability for the advection-diffusion equation where we treat the diffusion part using Crank-Nicholson and the advection part using FCTS (forward in time ...
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### finite volume for diffusion equation with anisotropic (tensor) coefficient

Consider the scalar PDE for $u$ with Dirichlet boundary conditions: $\mathrm{div}(\mathcal{K}\nabla u) = f\; \forall x\; \in \Omega \subset R^2$, $u = 0 \; \forall \; x\;\in \partial\Omega$ ...
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### The most efficient way to solve diffusion equation with concentrated initial condition

I want to solve the diffusion equation, i.e. $$\dot{f} - f'' = 0$$ with a boundary condition $f(0) = f(1) = 0$ and with an initial condition that $f$ is a boxcar function concentrated over some ...
694 views