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Fig. 1

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Two-dimensional sketch of possible AMR grid configurations at the interface between two levels. Left: configuration 1 where cell i is at level and cell i − 1 at level  + 1. Right: configuration 2 where cell i is at level and cell i − 1 at level  − 1. In both sketches, the vertical red line represents the surface over which energy is exchanged when level is updated. Similarly, the horizontal dashed red line represents the gradient over which the flux is computed using the energy marked by a red star (the value is interpolated using the value represented by the attached blue circle).

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