Numerical Hydrodynamics in Special Relativity.
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ABSTRACT: Electronic supplementary material
Supplementary material is available for this article at 10.12942/lrr-1999-3.
SUBMITTER: Marti JM
PROVIDER: S-EPMC5567266 | biostudies-literature | 1999
REPOSITORIES: biostudies-literature
Publications
Numerical Hydrodynamics in Special Relativity.
Living reviews in relativity 19991215 1
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discussed. An evaluation of the various numerical methods is given and future developments are analyzed.<h4>El ...[more]
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Project description:This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction.Electronic supplementary materialSupplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.
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Project description:The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A representative sample of available numerical schemes is discussed and particular emphasis is paid to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of relevant astrophysical simulations in strong gravitational fields, including gravitational collapse, accretion onto black holes and evolution of neutron stars, is also presented.Electronic supplementary materialSupplementary material is available for this article at 10.12942/lrr-2000-2.
| S-EPMC5256036 | biostudies-literature
Project description:The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them.Electronic supplementary materialSupplementary material is available for this article at 10.12942/lrr-2003-4.
| S-EPMC5660627 | biostudies-literature
Project description:This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works.Electronic supplementary materialSupplementary material is available for this article at 10.12942/lrr-2008-7.
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Project description:A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.
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Project description:Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
| S-EPMC3534154 | biostudies-literature
Project description:Numerical simulations are employed to study the hydrodynamics of self-propelled thunniform swimming. The swimmer is modeled as a tuna-like flexible body undulating with kinematics of thunniform type. The wake evolution follows the vortex structures arranged nearly vertical to the forward direction, vortex dipole formation resulting in the propulsion motion, and finally a reverse Kármán vortex street. We also carry out a systematic parametric study of various aspects of the fluid dynamics behind the freely swimming behavior, including the swimming speed, hydrodynamic forces, power requirement and wake vortices. The present results show that the fin thrust as well as swimming velocity is an increasing function of both tail undulating amplitude Ap and oscillating amplitude of the caudal fin θm. Whereas change on the propulsive performance with Ap is associated with the strength of wake vortices and the area of suction region on the fin, the swimming performance improves with θm due to the favorable tilting of the fin that make the pressure difference force more oriented toward the thrust direction. Moreover, the energy loss in the transverse direction and the power requirement increase with Ap but decrease with θm, and this indicates that for achieving a desired swimming speed increasing θm seems more efficiently than increasing Ap. Furthermore, we have compared the current simulations with the published experimental studies on undulatory swimming. Comparisons show that our work tackles the flow regime of natural thunniform swimmers and follows the principal scaling law of undulatory locomotion reported. Finally, this study enables a detailed quantitative analysis, which is difficult to obtain by experiments, of the force production of the thunniform mode as well as its connection to the self-propelled swimming kinematics and vortex wake structure. The current findings help provide insights into the swimming performance and mechanisms of self-propelled thunniform locomotion.
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Project description:A numerical hindcast of the macrotidal Loire Estuary (France) has been generated to provide a long-term dataset (2008-2018) of estuarine hydrodynamics, temperature, salinity, and sediment dynamics. This hindcast is based on simulations coupling water motion, wave and mixed sediment models, forced with realistic conditions and extensively validated in the salinity gradient and turbidity maximum areas. These data represent extremely valuable information for diverse scientific communities, providing (i) environmental parameters for ecosystemic studies along the Loire River-sea continuum, (ii) a singular estuarine configuration for inter-comparison of estuarine functioning, and (iii) a ten-year synoptical view of a major estuarine environment of the North Atlantic Ocean.
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Project description:The tides are a predictable, renewable, source of energy that, if harnessed, can provide significant levels of electricity generation. The Alderney Race (AR), with current speeds that exceed 5 m s-1 during spring tides, is one of the most concentrated regions of tidal energy in the world, with the upper-bound resource estimated at 5.1 GW. Owing to its significance, the AR is frequently used for model case studies of tidal energy conversion, and here we review these model applications and outcomes. We examine a range of temporal and spatial modelling scales, from regional models applied to resource assessment and characterization, to more detailed models that include energy extraction and array optimization. We also examine a range of physical processes that influence the tidal energy resource, including the role of waves and turbulence in tidal energy resource assessment and loadings on turbines. The review discusses model validation, and covers a range of numerical modelling approaches, from two-dimensional to three-dimensional tidal models, two-way coupled wave-tide models, Large Eddy Simulation (LES) models, and the application of optimization techniques. The review contains guidance on model approaches and sources of data that can be used for future studies of the AR, or translated to other tidal energy regions. This article is part of the theme issue 'New insights on tidal dynamics and tidal energy harvesting in the Alderney Race'.
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Project description:BackgroundThe calculation of diffusion-controlled ligand binding rates is important for understanding enzyme mechanisms as well as designing enzyme inhibitors.MethodsWe demonstrate the accuracy and effectiveness of a Lagrangian particle-based method, smoothed particle hydrodynamics (SPH), to study diffusion in biomolecular systems by numerically solving the time-dependent Smoluchowski equation for continuum diffusion. Unlike previous studies, a reactive Robin boundary condition (BC), rather than the absolute absorbing (Dirichlet) BC, is considered on the reactive boundaries. This new BC treatment allows for the analysis of enzymes with "imperfect" reaction rates.ResultsThe numerical method is first verified in simple systems and then applied to the calculation of ligand binding to a mouse acetylcholinesterase (mAChE) monomer. Rates for inhibitor binding to mAChE are calculated at various ionic strengths and compared with experiment and other numerical methods. We find that imposition of the Robin BC improves agreement between calculated and experimental reaction rates.ConclusionsAlthough this initial application focuses on a single monomer system, our new method provides a framework to explore broader applications of SPH in larger-scale biomolecular complexes by taking advantage of its Lagrangian particle-based nature.
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