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Fig. 1

image

Piecewise linear well-balanced reconstruction of the pressure. The pressure profile (black line) within the ith cell is decomposed into an equilibrium (blue line) and a perturbation part p(x) = p0,i(x) + p1,i(x). The equilibrium pressure p0,i(x) is simply given by Eq. (13). The point values of the perturbation are then computed at neighboring cell centers xi ± 1 by extrapolation of the equilibrium pressure reconstruction p0,i(xi ± 1). A piecewise linear monotonicity preserving reconstruction can then be applied to the pressure perturbation data, i.e., p1,i(xi ± 1) = pi ± 1p0,i(xi ± 1) and p1,i(xi) = 0.

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