New answers tagged finite-volume
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Finite volume method for 1D heat equation in 1D
The simple answer is, as I now realise, that you are free to compute the fluxes however you please, and the fluxes are evaluated on the cell boundaries, so I can just insert the actual values for the ...
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-1
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Approximation of derivatives in the finite volume method
The fluxes for this problem are evaluated on the cell boundaries rather than the cell centres. So for cells small enough, you can use a simple arithmetic average:
$$\frac{\partial \varphi}{\partial X}\...
- 131
1
vote
Accepted
Adding a diffusion term to the MUSCL - Kurganov and Tadmor central scheme
From a finite volume point of view, fluxes should be calculated at the cell faces and added up for each cell.
However, since you are using Cartesian meshes and your material properties are constant, ...
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1
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Approximation of derivatives in the finite volume method
The main idea behind the finite volume method is rather based on approximating the conservation laws in integral weak form (Divergence theorem)
\begin{equation}
\frac{d}{dt}\int_{x_L}^{x_R} u(x,t) ...
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-2
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Approximation of derivatives in the finite volume method
In a normal finite volue method you interpolate your profile by piecewise constant functions, so that in every cell you assume a constant value of amplitude for all points lying in that region. This ...
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