Source Of Gravity Research Articles

The torsion of stellar streams and the overall shape of galactic gravity's source

Flat rotation curves, $v(r)$, are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way's DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar.

Gravity: Where Quantum Physics and Classical Physics finally merge

In this 3rd paper of a triptych on quantum theory regarding gravity, quantum, and classical physics are merged seamlessly-however with conclusions deviating from classical physics regarding singularities, space-curvature, and graviton. Mathematically, singularities (Schwarzschild, Droste) vanish by proper definition of the gravity source and field descriptions acquiring full validity at the Planck scale. Space(-time) curvature is shown to be geodesic-trajectory curvature by (energy) objects in the field of (a) gravity source(s). The gravity field is found to be a scalar field in which the trajectories are defined only by the principle of least action (LaGrange, Feynman) by compensation of accelerations due to different physical causal sources of acceleration. The graviton is argued to be a massive Higgs-type scalar boson with ubiquitous presence since the creation of quantum and clustered mass in the universe: the influence of a settled gravity field on mass (in) entering this field, therefore, is instantaneous, i.e., unlike a vector boson description. Gravity waves, occurring in mergers/transitions of mass, are defined by changes in time of the gravity field (at max. c m/s) in space and only become observable when substantial mass/energy is involved due to the weakness and spatial decay of gravity fields. All mathematics (e.g. integral transformations, vector space, etc) and related operators in the paper are part of the Abelian group for validity at the Planck scale. Results thus constitute the description of gravity on all scales.‎‎

Experimental research on the thermal performance of the dry conduction plate for multi-point electronic chips

This paper designs a dry conductive heat dissipation method using several parallel heat pipes to solve the difficulty of the thermal management problem of multi-point electronic chips. The heat sources are distributed along the heat pipe, whose heat is efficiently conducted from the middle to the cold plate on the two sides. The effect of gravity, flow rate, and heat source distributions on the heat transfer performance is studied. The testing data indicated that gravity has less effect on the conduction performance of heat pipes for the cooling on two sides. As the heat sources concentrate in the centre, the heat pipe temperature difference between the centre and the side increases under the same transmission power. The results demonstrated that the two-side cooling and multi-point distribution heat conduction method is conducive to improving the thermal management capability under different inclination angles.

Universe inflation and nonlinear electrodynamics

We analyse the inflation of the universe when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics, with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.

Dimensionally continued black holes sourced by a conformally coupled scalar field and Chaplygin-like dark fluid

In this paper, we study the higher dimensional black holes of Lovelock gravity coupled with a conformal scalar field. The matter source of gravity is suggested to come from the Chaplygin-like dark fluid, i.e., the hybrid of a dark matter and dark energy. We primarily focus on dimensionally continued gravity where the coupling parameters are reduced into two independent parameters, i.e., the Newtonian and cosmological constants. In this specific case of Lovelock gravity, we derive the metric function that describes the hairy black holes surrounded by dark fluid. For these objects, the basic thermodynamic quantities are worked out. We discuss how the unified dark fluid affects both local and global thermodynamic stabilities. We also demonstrate that the radiation spectrum is proportional to the change in entropy of the hairy black holes. Lastly, the hairy black holes in the presence of Chaplygin-like dark fluid are briefly investigated within the context of generic Lovelock gravity.

Extension of the Schwarzschild black hole solution in f(R) gravitational theory and its physical properties

The successes of f(R) gravitational theory as a logical extension of Einstein’s theory of general relativity (GR) encourage us to delve deep into this theory and continue our study to attempt to derive an extension of the Schwarzschild black hole (BH) solution. In this study, in order to solve the output nonlinear differential equation, we closed the form of the system by assuming the derivative of f(R) with respect to the scalar curvature R to have the form F(r)=df(R(r))dR(r)=1-αr4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(r)=\\frac{\ extrm{d}f(R(r))}{\ extrm{d}R(r)}=1- \\frac{\\alpha }{r^4}$$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is a dimensional constant. Our study shows that when α→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 0$$\\end{document}, we obtain the Schwarzschild BH solution of GR assuming some constraints on the constant of integration, and if these constraints are bounded, we obtain the anti-de Sitter (AdS)/de Sitter (dS) spacetime. For the general case, i.e., when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0$$\\end{document}, we obtain a BH solution that tends asymptotically to AdS/dS spacetime. Moreover, we derive the timelike and null particle geodesics of the BH solution studied in this article. The equation of motion and effective potential of test particles are calculated to study the stability of radial orbits (trajectories). The energy and angular momentum are calculated to study the circular motion and stability of circular orbits. We also derive the stability condition using the geodesic deviation. Moreover, we discuss the physics of the output BH solutions through calculation of the thermodynamic quantities including entropy, the Hawking temperature, and Gibbs free energy. Finally, we check the validity of the first law of thermodynamics applied to the BH of this study. Although we can derive a Schwarzschild black hole solution in the lower order of f(R), specifically when f(R)=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)=R$$\\end{document}, where the gravitational mass is generated from the source of gravity, we demonstrate that in the higher orders of f(R), when f(R)≠R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)\ e R$$\\end{document}, the source of gravity is attributed primarily to higher-order corrections, and the source of gravity that was originally derived from the Schwarzschild black hole has ceased to be dominant.

Inertia, gravity and the meaning of mass

Our concept of mass has evolved considerably over the centuries, most notably from Newton to Einstein, and then even more vigorously with the establishment of the standard model and the subsequent discovery of the Higgs boson. Mass is now invoked in various guises depending on the circumstance: it is used to represent inertia, or as a coupling constant in Newton’s law of universal gravitation, and even as a repository of a mysterious form of energy associated with a particle at rest. But recent developments in cosmology have demonstrated that rest-mass energy is most likely the gravitational binding energy of a particle in causal contact with that portion of the Universe within our gravitational horizon. In this paper, we examine how all these variations on the concept of mass are actually interrelated via this new development and the recognition that the source of gravity in general relativity is ultimately the total energy in the system.

The big-bang started from nothing: Not the initially hot cosmic matter, but a positive vacuum pressure made the universe explode!

Mankind all over its past epochs did ask the question, how this huge and materially impressive universe could ever have started its existence. The standard dogmatic answer presently given by the majority of modern cosmologists is: By the Big-Bang! - i.e. that initial explosion of the central highly condensed world matter system! But why - it could be asked - should this system have exploded at all? Perhaps this popular BB-hypothesis of a general and global cosmic explosion creating the world is especially suggestive just in these days of wars and weapons all around. Nevertheless to declare such an initial event as the begin of the universe unexpectedly turns out to be extremely hard to explain when based on purely physical grounds. Though it is easy to envisage a granate explosion causing matter to fly apart in all directions from the center of the explosion, but as a total surprise it is extremely hard to explain which physically operating forces or pressures might be responsible to drive the initially highly compacted cosmic matter agglomeration apart of each other. If the explosion forces are imagined as due to acting thermal pressure forces of normal massive matter, then the needed pressures cannot be due to the extremely high temperatures of the condensed matter, because the thermal energy of relativistically hot matter, as relativity theory tells us, will act as an additional source of gravity, i.e. making matter even "heavier"! Hence this just impedes the initial mass agglomeration to explode and fly apart. As we shall show in the following article the explosive BB- event can only physically be explained, if the necessary pressure is not conventionally realized by the temperature of the gravitating matter, but to the contrary by the immaterial cosmic vacuum. In fact - as we shall demonstrate here - without a cosmic vacuum pressure, the so-called Big-Bang never at all could have happened. Certainly vacuum pressure up to the present days of cosmology still is a fully speculative subject, but it will become evident in the following article, that without this highly speculative, physically handable quantity a primordial Big-Bang would not have happened at all.

Constraining the Structure under Lunar Impact Basins with Gravity

The lunar gravity field is used to estimate and constrain the depth of mass anomalies under 19 major lunar impact basins. We use radial gravitational spectra, consisting of accelerations computed either per spherical harmonic degree or cumulatively, at surface locations to obtain the distribution of the gravity signal with spherical harmonic degree and, by implication, to the likely depth below the surface. The results provide estimates for the maximum likely depths of the primary component to the mass anomalies under 19 basins. We find that the maximum depths of the primary source of mascon gravity on the lunar nearside are deeper than the depths for those on the farside when South Pole–Aitken (SPA) is excluded. All basin mass anomalies on the lunar nearside are in the mantle. The maximum depth of the primary source of the mass anomalies is <80 km, with the exception of SPA, whose dominant mass signature lies at a maximum depth of >200 km beneath the surface. The upper 20 km under all basins is largely devoid of anomalies, reflecting predominantly mixing and relaxation associated with impact melt combined with ejecta fallback, as well as homogenization associated with post-basin formation impact bombardment. Except for SPA, all basin anomalies merge with the deep interior at ∼150 km or below, indicating the depth penetration of disruption of the density structure of the lunar interior associated with impact bombardment.

A linear low effort stabilization method for the Euler equations using discontinuous Galerkin methods

SummaryWe present a novel and simple yet intuitive approach to the stabilization problem for the numerically solved Euler equations with gravity source term relying on a low‐order nodal Discontinuous Galerkin Method (DGM). Instead of assuming isothermal or polytropic solutions, we only take a hydrostatic balance as a given property of the flow and use the hydrostatic equation to calculate a hydrostatic pressure reconstruction that replaces the gravity source term. We compare two environments that both solve the Euler equations using the DGM: deal.II and StormFlash. We utilize StormFlash as it allows for the use of the novel stabilization method. Without stabilization, StormFlash does not yield results that resemble correct physical behavior while the results with stabilization for StormFlash, as well as deal.II model the fluid flow more accurately. Convergence rates for deal.II do not match the expected order while the convergence rates for StormFlash with the stabilization scheme (with the exceptions for the L errors for momentum) meet the expectation. The results from StormFlash with stabilization also fit reference solutions from the literature much better than those from deal.II. We conclude that this novel scheme is a low cost approach to stabilize the Euler equations while not limiting the flow in any way other than it being in hydrostatic balance.

Gravity Application to Obtain the Subsurface Structures of Mafid Region, North Nasser Lake, Egypt

This study aims to define structures below the surface of the Mafid Area by using gravity data interpretation. Estimates were made for the contact density contrast and the gravity sources' depths. The source depths and contact locations were estimated using the Euler deconvolution method. Structures with shallow and deep seats were also assessed using power spectrum analysis. The structure at a shallow depth was between 0.032 km and 0.437 km. According to the Euler deconvolution method's outcomes, the basement may be below ground in the area's southernmost portion, and it has grown to between 200 and 300 meters in the area's northernmost portion. Multiple faults affect the region that most trends in the NW-SE, NNW-SSE, E-W, NE-SW, and NNE-SSW directions, according to the structural map that has been interpreted. Three-dimensional gravity modelling shows that the upper surface depth of crystalline rocks (Basement rocks ) ranges from 170 to 374 m.

The universe generated by the explosion of the primordial cosmic vacuum!

Over all its epochs mankind always has put the fundamental question: When and why at all did the universe start its existence? Most cosmologists univocally do answer this question with the standard dogmatic answer: By the Big-Bang! - namely by the initial explosion of an extremely concentrated world matter system! This standard paradigm of a general and global explosion creating this world obviously appears to be highly suggestive, though such an explosive event unexpectedly turns out to be extremely hard to understand on purely physical grounds. This is because it is extremely hard to explain which pressures might be responsible to drive the initially highly compacted cosmic matter apart. The somewhat naive idea that the required explosion forces in view of the extremely high temperatures and the extreme highly compacted primordial cosmic matter, are due to extreme initial pressure forces does not solve the problem, because relativistically hot matter will be just an additional source of gravity, hence just contrary to the expectations impedes matter to fly apart. It can, however, be shown that the expected explosive BB- event can only physically occur, if the required pressure is not established by the temperature of gravitating matter, but by the cosmic vacuum. In fact we show that without this cosmic vacuuum pressure, the so-called Big-Bang never could have happened, even though vacuum pressure up to the present days of cosmology, still may be a rather speculative subject. In the following article we shall demonstrate that with a revised understanding of this highly speculative quantity one can explain the present universe as an explosion of the primordial cosmic vacuum followed by a succesive materialisation of this vacuum into cosmic matter at the ongoing cosmic expansion.

Sectorial Paley–Wiener theorem

We consider the problem of restoring a two‐dimensional convex source of gravity based on values of its potential function on a union of half‐planes. With that aim we prove a Paley–Wiener type theorem for functions of exponential type in a sector. In particular, we find the maximal set of analytic continuation whose complement is convex inside a sector. Our result serves as a sectorial analog of G. Polya's indicator theorem. It corrects, simplifies, and extends a result of M. Morimoto. It also improves a related result of M. Dzhrbashyan and A. Avetisyan.

Never there would have been a cosmic big-bang without the action of a vacuum pressure!

The fundamental and always resurrecting question of mankind, how this universe could ever have started its existence, is answered by most cosmologists with the standard dogmatic answer: By the Big-Bang! - that initial explosion of the world matter system! Perhaps this standard paradigm of a general and global explosion creating the world, especially in these days of wars and weapons all around, seems to be highly suggestive. Nevertheless such an event unexpectedly turns out to be extremely hard to explain as based on purely physical grounds. It indeed seems easy to imagine a granate explosion causing matter to fly apart in all directions, but it is extremely hard to explain which pressures might be responsible to drive the initially highly compacted cosmic matter apart of eachother. If the explosion forces are imagined as due to pressure forces then these pressures cannot be due to extremely high temperatures of matter, because relativistically hot matter will be just an additional source of gravity, hence just impeding matter to fly apart. As we shall show in the following article the explosive BB- event can only physically be explained, if the necessary pressure is not manifested by the gravitating matter, but by the cosmic vacuum. In fact without the cosmic vacuuum pressure, the so-called Big-Bang never could have happened. Vacuum pressure, however, up to the present days of cosmology, still is a fully speculative subject, but it will become evident in the following article, that without this highly speculative quantity there could not have happened a Big-Bang at all.

Magnetized Black Holes: Interplay between Charge and Rotation

Already in the cornerstone works on astrophysical black holes published as early as in the 1970s, Ruffini and collaborators have revealed the potential importance of an intricate interaction between the effects of strong gravitational and electromagnetic fields. Close to the event horizon of the black hole, magnetic and electric lines of force become distorted and dragged even in a purely electro-vacuum system. Moreover, as the plasma effects inevitably arise in any astrophysically realistic environment, particles of different electric charges can separate from each other, become accelerated away from the black hole or accreted onto it, and contribute to the net electric charge of the black hole. From the point of principle, the case of super-strong magnetic fields is of particular interest, as the electromagnetic field can act as a source of gravity and influence spacetime geometry. In a brief celebratory note, we revisit aspects of rotation and charge within the framework of exact (asymptotically non-flat) solutions of mutually coupled Einstein–Maxwell equations that describe magnetized, rotating black holes.

Can the Present-Day Cosmology Really Make the Universe Understandable as a Sheer Physical System Operating as it must?

The modern and present day cosmology starts from the main idea, that our universe had one common begin in the so-called "Big-Bang", and that the traces of this begin can be clearly extrapolated from the presently observable cosmic facts, which still now can be found in the universe. In addition one assumes, based on the "cosmologic principle" that no space point in this universe is privileged with respect to any others, rather this universe in its energy depositions and physical conditionings represents itself as a totally homogeneous building in which everywhere happens the same, i.e. for all space points the past, the presence and the future are identical in this universe - at least when studied on reasonably large space- and time- dimensions and when studied on such "reasonable" dimensions it is subject to a common and ubiquitously identical evolution, bringing up the same future simultaneously at all of its places [1-3]. In this article here, we shall subject this standard cosmologic view to an extended critical exam in order to expose its rational weaknesses and intellectual impudence’s. It will be shown that the upcoming fate of the present universe strongly depends on its present internal Hubble expansion dynamics and its internal cosmic ingredients, which influence this expansion dynamics. Amongst these latter ingredients, one finds the mass content of the universe which by its gravitational attraction decelerates the cosmic expansion, and its opponent, the vacuum energy, that is seen as an enigmatic physical phenomenon which accelerates the cosmic expansion. We will show, however, that both these obviously essential cosmic ingredients are only poorly understood. Especially this concerns the mysterious vacuum energy of which we demonstrate that acceleration of cosmic dynamics can only be connected with pressure, but if vacuum pressure accelerates the expansion of the universe and so does perform thermodynamic work, it then cannot be constant as once proposed by Einstein and thus as such taken for granted by [4]. In addition, the internal cosmic gravity as we show is only poorly understood especially what concerns the source of this internal gravity, which usually is ascribed to the mass content of the universe connected with the mean cosmic mass density. Just this latter quantity, however, is a highly problematic physical quantity as we intensively demonstrate in this article. Taking everything together it is therefore hard to feel safe in this "explained universe" which cosmologists presently are offering to the community as their understanding of how this cosmos works

Thermal instability analysis in magneto-hybrid nanofluid layer between rough surfaces with variable gravity and space-dependent heat source

The onset of thermal instability with hybrid nanoparticles Al2O3–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters ([Formula: see text]), Darcy number (Da), gravity variation function ([Formula: see text]), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number [Formula: see text] which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ([Formula: see text]) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and [Formula: see text] (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Precession of bounded orbits and shadow in quantum black hole spacetime

The geodesics around compact objects are one of the best tools to understand the geometrical properties of the central gravity source. In this paper, we study timelike and lightlike geodesics of a quantum black hole proposed in [E. Binetti et al., Phys. Rev. D 106, 046006 (2022).], which does not require committing to a specific model of quantum gravity. We analyze the quantum correction on the related obsrevables: periapsis precession of bounded orbits and angular shadow size. We find that, compared to the classical case, the quantum correction will enhance the periapsis precession as well as the black hole shadow. This effect is more significant for a smaller quantum black hole.

Космологическая модель с квантовым туннелированием

The cosmological model with expansion and rotation with Bianchi type II metric is constructed within the framework of general relativity. The source of gravity of the model is an accompanying aniso-tropic fluid. The Wheeler–DeWitt equation is derived. The possibility of minisuperdimensional quantization of the model is considered. The tunneling wave function and the tunneling coefficient are found.

A Well-Balanced HLL Scheme for Hyperbolic Conservation Systems With Source Terms

This paper presents new finite volume schemes for hyperbolic conservation system with source terms. The classical finite volume schemes could not accurately simulate the dynamic problems caused by the balance between flux term and source terms. In order to deal with this problem, an approximate Riemann solver with source terms was designed in accordance with the classical HLL approximation Riemann solver. The well-balanced HLL schemes (WB-HLL) was obtained by modifying the flux calculation schemes for one-dimensional Euler equations and ideal MHD with gravity source terms, and a proof for well-balanced property of the new schemes has been presented.Two numerical examples of one-dimensional Euler equation and ideal MHD demonstrated that the WB-HLL scheme has higher accuracy and faster convergence than the classical HLL.