Constraint propagation of C2-adjusted formulation. II. Another recipe for robust Baumgarte-Shapiro-Shibata-Nakamura evolution system

Takuya Tsuchiya, Gen Yoneda, Hisa Aki Shinkai

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    2 Citations (Scopus)

    Abstract

    In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura equations. The idea is to add functional derivatives of the norm of constraints, C2, to the evolution equations, which was proposed by Fiske (2004) and was applied to the ADM formulation in our previous study. We derive the constraint propagation equations, discuss the behavior of constraint damping, and present the results of numerical tests using the gauge-wave and polarized Gowdy wave spacetimes. The construction of the C2-adjusted system is straightforward. However, in BSSN, there are two kinetic constraints and three algebraic constraints; thus, the definition of C2 is a matter of concern. By analyzing constraint propagation equations, we conclude that C2 should include all the constraints, which is also confirmed numerically. By tuning the parameters, the lifetime of the simulations can be increased 2-10 times longer than those of the standard Baumgarte-Shapiro-Shibata-Nakamura evolutions.

    Original languageEnglish
    Article number044018
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume85
    Issue number4
    DOIs
    Publication statusPublished - 2012 Feb 8

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    formulations
    propagation
    norms
    damping
    tuning
    life (durability)
    kinetics
    simulation

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

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    abstract = "In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura equations. The idea is to add functional derivatives of the norm of constraints, C2, to the evolution equations, which was proposed by Fiske (2004) and was applied to the ADM formulation in our previous study. We derive the constraint propagation equations, discuss the behavior of constraint damping, and present the results of numerical tests using the gauge-wave and polarized Gowdy wave spacetimes. The construction of the C2-adjusted system is straightforward. However, in BSSN, there are two kinetic constraints and three algebraic constraints; thus, the definition of C2 is a matter of concern. By analyzing constraint propagation equations, we conclude that C2 should include all the constraints, which is also confirmed numerically. By tuning the parameters, the lifetime of the simulations can be increased 2-10 times longer than those of the standard Baumgarte-Shapiro-Shibata-Nakamura evolutions.",
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    AU - Yoneda, Gen

    AU - Shinkai, Hisa Aki

    PY - 2012/2/8

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    N2 - In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura equations. The idea is to add functional derivatives of the norm of constraints, C2, to the evolution equations, which was proposed by Fiske (2004) and was applied to the ADM formulation in our previous study. We derive the constraint propagation equations, discuss the behavior of constraint damping, and present the results of numerical tests using the gauge-wave and polarized Gowdy wave spacetimes. The construction of the C2-adjusted system is straightforward. However, in BSSN, there are two kinetic constraints and three algebraic constraints; thus, the definition of C2 is a matter of concern. By analyzing constraint propagation equations, we conclude that C2 should include all the constraints, which is also confirmed numerically. By tuning the parameters, the lifetime of the simulations can be increased 2-10 times longer than those of the standard Baumgarte-Shapiro-Shibata-Nakamura evolutions.

    AB - In order to obtain an evolution system which is robust against the violation of constraints, we present a new set of evolution systems based on the so-called Baumgarte-Shapiro-Shibata-Nakamura equations. The idea is to add functional derivatives of the norm of constraints, C2, to the evolution equations, which was proposed by Fiske (2004) and was applied to the ADM formulation in our previous study. We derive the constraint propagation equations, discuss the behavior of constraint damping, and present the results of numerical tests using the gauge-wave and polarized Gowdy wave spacetimes. The construction of the C2-adjusted system is straightforward. However, in BSSN, there are two kinetic constraints and three algebraic constraints; thus, the definition of C2 is a matter of concern. By analyzing constraint propagation equations, we conclude that C2 should include all the constraints, which is also confirmed numerically. By tuning the parameters, the lifetime of the simulations can be increased 2-10 times longer than those of the standard Baumgarte-Shapiro-Shibata-Nakamura evolutions.

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