Numerical Relativity is a coupled set of partial differential equations
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Direct formulation has 10 independent equations
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Some implementations have up to 50 coupled functions
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Equations can be divided into two classes
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4 Elliptic (Laplace equation-like) constraint equations which must be satisfied at each time
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6 coupled Hyperbolic (Wave equation like) equations describing time evolution
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For CFD, the "physics" determines computational issues
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e.g. a shock represents a rapidly varying solution which requires typically an adaptive irregular mesh and finite element solution method
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For Numerical relativity, one can change the nature of solution by changing "space itself"
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This is called choosing the Gauge
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One gauge could have rapidly varying fields and require adaptive finite elements
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Another Gauge could have slowly varying fields and be soluble with finite difference.
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