Spline Techniques for Solving Relativistic Conservation Equations

Abstract

We discuss a new numerical method for solving the relativistic hydrodynamic equations based upon the basis-spline collocation approach. Analytical and numerical results are compared for several problems, including one-dimensional expansions and collisions for which analytical solutions exist. Our methods, which may be easily and massively parallelized, are shown to give numerical results which agree to within a few percent of the analytic solutions. We discuss the relevance of the υ = z/t scaling solutions for the one-dimensional problem when applied to relativistic heavy-ion collisions. Finally, we discuss applications to three-dimensional problems, and present results for a typical three-dimensional expansion.

Numerical Hydrodynamics in Special Relativity

“…When tested against 1D relativistic shock tubes all these codes performed similar to the code of Wilson. More recently, Dean et al [69] have applied flux correcting algorithms for the SRHD equations in the context of heavy ion collisions. Recent developments in relativistic SPH methods [53, 261] are discussed in Section 4.2.…”

Numerical Hydrodynamics in Special Relativity

“…When tested against 1D relativistic shock tubes all these codes performed similar to the code of Wilson. More recently, Dean et al [ 39 ] have applied flux correcting algorithms for the SRHD equations in the context of heavy ion collisions. Recent developments in relativistic SPH methods [ 30 , 164 ] are discussed in Section 4.2 .…”

High Order Central Schemes Applied to Relativistic Multi-Component Flow Models

“…In mid eighties, Norman and Winkler [5] proposed a reformulation of the difference equations with artificial viscosity consistent with relativistic dynamics of non-perfect fluids. Dean et al [6] used flux correcting algorithms for RGD equations in the context of heavy ion collisions.A good introduction about the recent methods applied to RGD can be found in the review article of Martí and Müller [7]. Some popular methods which are extended for RGD and are also discussed in [7] are the Rao methods [8] used by Eulderink et al [9] [10], PPM method [11] by Martí and Müller [12], Glimm's methods [13] by Wen et al [14], HLL method [15] by Schneider et al [16], Marquina flux formula [17] by Martí et al [12] [18] and relativistic beam scheme [19] by Yang et al [20].…”

“…In mid eighties, Norman and Winkler [5] proposed a reformulation of the difference equations with artificial viscosity consistent with relativistic dynamics of non-perfect fluids. Dean et al [6] used flux correcting algorithms for RGD equations in the context of heavy ion collisions.…”