Primitive Variable Determination in Conservative Relativistic Magnetohydrodynamic Simulations

In nonrelativistic hydrodynamics and magnetohydrodynamics, conservative integration schemes for the fluid equations of motion are generally employed. The computed quantities, namely, the mass density, (vector) momentum density, and energy density, can readily be converted back into the primitive variables that define the problem, namely, the mass density, (vector) velocity, and thermal pressure. In practical terms, the primitive variables can be “peeled away” from the computed variables. In relativistic problems, however, the appearance of the Lorentz factor in the computed quantities dramatically complicates the problem owing to its near-singular dependence upon relativistic velocities. Conservative integration schemes for the hyperbolic partial differential equations of special relativistic magnetohydrodynamics (RMHD) yield estimates of the five conserved quantities that are related in a highly nonlinear way to the five primitive variables. We also observe that an equivalent set of five nonlinear equati...