Relativistic Shock Hydrodynamics

The special-relativistic equations for a perfect fluid are differenced in characteristic form. Since information concerning the state of a fluid is propagated along the characteristic directions, the differencing procedure preserves a fundamental property of the hydrodynamic equations. Shocks are calculated using an energy Lagrange frame where energy fractions become a coordinate. Since numerical zones are attached to surfaces of constant energy, they move so as to conserve the total energy outside a surface and hence strong shocks appear stationary in this frame. The jump conditions across the shock can be enforced directly, so the need for an artificial viscosity to spread the shock over several mass Lagrange zones is eliminated. The result is an order-of-magnitude reduction in computation for equivalent accuracy. On the other hand, the differencing of the equations in characteristic form using a mass Lagrange frame is particularly well suited to the problem of expansion of a relativistic fluid into vacuum. Examples are given of calculations of shocks and expansions that agree in detail with analytical solutions. Subject headings: hydrodynamics - relativity - shock waves