... slope¹

the derivative of the dynamical variable, page 61 [10]

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...$A(t)B(x)$²

Under the assumption both functions are continuous, smooth, etc. etc

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...exact_triangle.f³

This subroutine is called by main.f to output a sdf for the exact solution named G2exact_triangleC_lev4.sdf( depends on the level of discretization of course)

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... conditions⁴

The ultra-relativistic fluid (we assume that the internal energy density of the fluid is much larger than the rest mass density, i.e. $\rho_o \epsilon \gg \rho_o$) for which the equation of state is:

$$P=\left(\Gamma-1 \right) \rho,$$ (52)

being $\Gamma$ the adiabatic index. We will consider $\Gamma$ to be constant. Note that because of this approximation the rest mass density becomes dynamically unimportant allowing us to drop equation (49) from the system. Therefore the only equations that we need to consider are (50)

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... state⁵

Meaning that the speed of sound is less than the speed of light

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