Numerical simulations in gravitation and astrophysics are computational techniques that solve the governing equations of gravitational dynamics—typically Einstein’s field equations of general relativity or the Newtonian/relativistic N-body problem—using discretization schemes such as finite difference, finite volume, spectral, or particle-based methods. They enable quantitative modeling of systems like compact-object binaries, gravitational-wave sources, stellar evolution, accretion flows, galaxy formation, and large-scale structure. These simulations incorporate additional physics (e.g., magnetohydrodynamics, radiation transport, nuclear microphysics) and employ high-performance computing, adaptive mesh refinement, and sophisticated time-integration algorithms to resolve multi-scale, nonlinear phenomena inaccessible to purely analytic approaches.
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