Search results for "Shock capturing method"

showing 5 items of 5 documents

Shock capturing methods in 1D numerical relativity

2008

A numerical code is presented which uses modern shock capturing methods to evolve spherically symmetric perfect fluid space-times. Harmonic slicing is used to ensure singularity avoidance, which is crucial in strong field situations. Some tests are presented, including an application to the stellar collapse problem.

PhysicsGravitational time dilationNumerical relativityClassical mechanicsTheory of relativityShock capturing methodRelativistic mechanicsPerfect fluidMechanicsIntroduction to the mathematics of general relativityTheoretical motivation for general relativityComputingMethodologies_COMPUTERGRAPHICS
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Power ENO methods: a fifth-order accurate Weighted Power ENO method

2004

In this paper we introduce a new class of ENO reconstruction procedures, the Power ENO methods, to design high-order accurate shock capturing methods for hyperbolic conservation laws, based on an extended class of limiters, improving the behavior near discontinuities with respect to the classical ENO methods. Power ENO methods are defined as a correction of classical ENO methods [J. Comput. Phys. 71 (1987) 231], by applying the new limiters on second-order differences or higher. The new class of limiters includes as a particular case the minmod limiter and the harmonic limiter used for the design of the PHM methods [see SIAM J. Sci. Comput. 15 (1994) 892]. The main features of these new ENO…

Numerical AnalysisConservation lawPhysics and Astronomy (miscellaneous)Applied MathematicsMathematical analysisScalar (physics)Harmonic (mathematics)Computer Science ApplicationsEuler equationsMaxima and minimaComputational Mathematicssymbols.namesakeDiscontinuity (linguistics)Riemann problemModeling and SimulationShock capturing methodsymbolsMathematicsJournal of Computational Physics
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Computing Strong Shocks in Ultrarelativistic Flows: A Robust Alternative

1999

In recent years, shock capturing methods have started to be used in numerical simulations in Relativistic Fluid Dynamics (RFD). These techniques lead to explicit numerical codes that are able to successfully simulate the extreme conditions of the ultrarelativistic regime. After [2], an explicit, ready-to-use description of the full spectral decomposition of the Jacobian matrices of the RFD system is available, and this allows us to implement Marquina’s scheme [3] in RFD. The scheme is seen to maintain the good behavior shown in [3] with respect to certain numerical pathologies.

Physics::Fluid DynamicsPhysicssymbols.namesakeShock capturing methodJacobian matrix and determinantsymbolsStatistical physicsRelativistic fluidMatrix decomposition
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A Polynomial Approach to the Piecewise Hyperbolic Method

2003

In this paper, a local (third-order accurate) shock capturing method for hyperbolic conservation laws is presented. The method has been made with the same idea as the PHM method, but with a simpler reconstruction. A comparison with the classic high order methods is discussed.

Conservation lawPolynomialMechanical EngineeringHyperbolic functionMathematical analysisComputational MechanicsEnergy Engineering and Power TechnologyAerospace EngineeringCondensed Matter PhysicsMechanics of MaterialsShock capturing methodPiecewiseHigh orderHyperbolic partial differential equationMathematicsInternational Journal of Computational Fluid Dynamics
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Riemann solvers in relativistic astrophysics

1999

AbstractOur contribution reviews High Resolution Shock Capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. One objective of our contribution is to show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. We will review recent literature concerning the main properties of different special relativistic Riemann solvers, and disc…

Conservation lawPartial differential equationApplied MathematicsRiemann solverLorentz factorsymbols.namesakeTheoretical physicsRiemann hypothesisComputational MathematicsRiemann problemFlow (mathematics)Shock capturing methodsymbolsMathematicsMathematical physicsJournal of Computational and Applied Mathematics
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