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Questions tagged [axisymmetric]

Problems with axial (radial) symmetry that arise in cylindrical geometries (can also be hollow).

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How to derive the deformation matrix $F$ of axisymmetric problem?

I am working on a 2D axisymmetric problem and am wondering how to derive the gradient operation matrix for an element and the deformation matrix, I have no clue how to do it and after searching on the ...
2 votes
1 answer

FEM for a biphasic drying problem

I have the following PDE originating from a biphasic drying model, where $\xi \in [0,\Xi]$ is a radial coordinate attached to the dry skeleton of a wet cylindrical body: $$ \frac{\partial u}{\partial ...
6 votes
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Numerical artefacts in solution of spherical heat equation using FDM

I was attempting to solve the diffusion equation for a solid sphere using a naive FDM scheme. The governing PDE for the scalar concentration field $u(r,t)$ is $$ u_t = r^{-2}(r^2 \alpha u_r)_r, \quad ...
2 votes
1 answer

Objective function for PDE-constrained boundary control problem in cylindrical coordinates

I'm interested in solving a boundary control problem for an axisymmetric diffusion problem where diffusive fluxes only appear radially. The corresponding problem for a uni-dimensional slab can be ...