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Foil 15 CPS713 Case Study II) Computational Features of Numerical Relativity (Contd) -- Singularity Structure

From Overview of CFD and Numerical Relativity Case Study CPSP713 -- Autumn Semester 1994. by Geoffrey C. Fox
1 There are no small coefficients of second order derivative terms
  • In CFD small coefficient proportional to viscosity led to rapidly varying fields so product of viscosity times second derivative was comparable in size to other terms in CFD equations
  • This leads to shocks, boundary layers, turbulent flow in CFD i.e.
    • CFD has singularities which are lower dimension than solution space
2 Numerical Relativity has the world's most significant singularity -- Black Holes
  • Otherwise singularities are volume based and not like shocks
  • Correspondingly Numerical Relativity can use finite difference methods
    • One does need adaptive block structured meshs but probably not unstructured meshs
    • Can use Finite Elements (FEM) and may be preferable -- CFD is more or less required to use FEM
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