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A simple second order cartesian scheme for compressible Euler flows

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Figure

Figure 1: Mesh points and zero level set. The red segment represents ϕ = 0;
Figure 2: Example of geometric configuration at the interface. A is the interface point located between (i, j) and (i + 1, j)
Figure 3: Cells and stencils used for the extrapolation state, considering u ∗ n > 0.
Figure 4: Illustration of the determination of ghost-cell variables.
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