The essential ingredients of a numerical relativity code are the evolution formalism and the numerical scheme. We have already discussed a couple of well-tested evolution formalisms: the generalized harmonic one and Z4, from which BSSN can be derived by symmetry breaking. We have also presented a robust, cost-efficient, finite-difference scheme (FDOC), which is able to evolve smooth solutions, and a more sophisticated alternative (MUSCL), suitable for weak solutions.
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Bona, C., Bona-Casas, C., Palenzuela-Luque, C. (2009). Black Hole Simulations. In: Elements of Numerical Relativity and Relativistic Hydrodynamics. Lecture Notes in Physics, vol 783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01164-1_6
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