Abstract
The dynamics of inviscid multi-component relativistic fluids may be modeled by the relativistic Euler equations, augmented by one (or more) additional species equation(s). We use the high-resolution staggered central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. The current schemes can handle strong shocks and the oscillations near the interfaces are negligible, which usually happens in the multi-component flows. The schemes also guarantee the exact mass conservation for each component, the exact conservation of total momentum, and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validate the application of these schemes to relativistic multi-component flows.
Highlights
Relativistic gas dynamics plays an important role in areas of astrophysics, high energy particle beams, high energy nuclear collisions, and free-electron laser technology
We present one- and two-dimensional numerical problems in order to validate the application of central schemes for the solution of multi-component flow problems
The equilibrium states for each component are coupled in space and time to have a common temperature and velocity
Summary
Relativistic gas dynamics plays an important role in areas of astrophysics, high energy particle beams, high energy nuclear collisions, and free-electron laser technology. How to cite this paper: Ghaffar, T., et al (2014) High Order Central Schemes Applied to Relativistic Multi-Component Flow Models. All these methods are mostly developed out of the existing reliable methods for solving the Euler equations of non-relativistic or Newtonian gas dynamics. We use the high-resolution non-oscillatory central schemes of Nessyahu and Tadmor [30] as well as Jiang and Tadmor [31] to solve these Euler equations. The central schemes are predictor-corrector methods which consist of two steps: starting with given cell averages, we first predict point values which are based on the non-oscillatory piecewise-linear reconstructions from the cell averages. At the second corrector step, we use staggered averaging, together with the predicted mid values, to realize the evolution of these averages This results in a second-order, non-oscillatory central scheme.
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