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Foil 12 CPS713 Case Study II) Computational Features of Numerical Relativity (Contd) -- Singularity Structure
From Overview of Monte Carlo Case Study CPSP713 -- Autumn Semester 1994. byGeoffrey C. Fox, Paul Coddington
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
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
