The space–time CE/SE method for solving ultra-relativistic Euler equations

Qamar, Shamsul; Yousaf, Muhammad; Mudasser, Sidrah

doi:10.1016/j.cpc.2010.12.044

Cited by 5 publications

(2 citation statements)

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“…This can be used for the construction of numerical schemes which preserve positive pressure and satisfy a discrete version of the entropy inequality, see [10,11,13]. Some other analytical and numerical methods for the ultra relativistic Euler equations are studied in [1,2,3,8,12,15,16,17,18]. Recently numerical results using central upwind scheme are reported in [7] for one and two dimensional special ultra-relativistic Euler equations.…”

Section: Introductionmentioning

confidence: 99%

Radially symmetric solutions of the ultra-relativistic Euler equations

Kunik¹,

Liu²,

Warnecke³

2020

Preprint

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The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure p, the spatial part u ∈ R 3 of the dimensionless four-velocity and the particle density n. Radially symmetric solutions of these equations are studied. Analytical solutions are presented for the linearized system. For the original nonlinear equations we design and analyze a numerical scheme for simulating radially symmetric solutions in three space dimensions. The good performance of the scheme is demonstrated by numerical examples. In particular, it was observed that the method has the capability to capture accurately the pressure singularity formation caused by shock wave reflections at the origin.

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Section: Introductionmentioning

confidence: 99%

Radially symmetric solutions of the ultra-relativistic Euler equations

Kunik¹,

Liu²,

Warnecke³

2020

Preprint

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“…A part from the kinetic scheme which is based on kinetic equation and equilibrium distribution function [ 10 – 14 ], all these techniques are based on the macroscopic continuum description. Moreover, Qamar and Yousaf have implemented the space-time CESE method [ 15 , 16 ] and discontinuous Galerkin finite element method [ 17 ] for solving these RHD equations.…”

Section: Introductionmentioning

confidence: 99%

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

2015

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The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems.

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