arXiv subjects

Harish Kumar

Publications and source records attributed to Harish Kumar.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Hybrid WENO Schemes for Special Relativistic Hydrodynamics with Adaptive Characteristic Reconstruction

Special relativistic hydrodynamics (SRHD) equations arise in the modeling of high-speed fluid flows encountered in astrophysical phenomena such as jets, supernova explosions, and gamma-ray bursts. Owing to their highly nonlinear hyperbolic nature, solutions often develop strong discontinuities, making the design of stable and accurate numerical schemes challenging. Although Weighted Essentially Non-Oscillatory (WENO) schemes are widely used for such problems, component-wise WENO reconstruction may produce spurious oscillations near discontinuities. On the other hand, characteristic-wise WENO reconstruction provides accurate non-oscillatory solutions for systems of conservation laws, but it involves the computation of eigenvectors in each cell, which leads to high computational cost. In this work, we intend to develop hybrid schemes which maintain the non-oscillatory feature of characteristic-wise WENO while being less costly. We propose three hybrid schemes, namely the H1-WENO, H2-WENO, and H3-WENO schemes, based on a new troubled-cell indicator constructed from the smoothness indicators of the WENO scheme. The proposed troubled-cell indicator effectively distinguishes smooth and discontinuous regions, allowing the hybrid schemes to employ inexpensive reconstructions in smooth regions and the characteristic-wise WENO reconstruction only near discontinuities. Numerical experiments demonstrate that the proposed schemes retain the accuracy and robustness of characteristic-wise WENO methods while significantly reducing the computational cost. In particular, the H1-WENO scheme achieves an approximately 30--40% improvement in computational efficiency compared to the standard WENO scheme in 2D test cases.

math.NA↗

arXiv2026

Entropy stable finite difference schemes for One-Fluid Two-Temperature Euler Non-equilibrium Hydrodynamics

In this work, we consider the One-Fluid Two-Temperature Euler (OFTT-Euler) equations used for modeling non-equilibrium hydrodynamics. The model comprises a system of nonlinear hyperbolic partial differential equations with non-conservative products. The model decomposed the total pressure into two scalar components: one for electrons and one for ions. Our aim in this work is to design entropy-stable finite difference numerical schemes for the model. This is achieved by reformulating the equations such that the reformulated non-conservative part does not contribute to the entropy. Then, we design higher-order entropy-conservative numerical schemes by using Tadmor's relation for the conservative part and higher-order central differences for the non-conservative parts. Finally, we design the entropy-dissipation terms using the entropy-scaled right eigenvectors of the conservative part, thereby deriving the entropy inequality for the entire system. We present several test cases in one and two dimensions to demonstrate the accuracy and stability of the proposed schemes.

math.NA↗

arXiv2026

Admissible Lax-Wendroff Flux Reconstruction Method with Automatic Differentiation on Adaptive Curved Meshes for Relativistic Hydrodynamics

The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these sharp waves effectively requires a mesh with high resolution, making the scheme computationally expensive. In this work, adaptive mesh refinement is used with the high-order Lax-Wendroff flux reconstruction (LWFR) method to solve the system of RHD equations, which is closed with general equations of state. To make the scheme Jacobian-free, the idea of automatic differentiation is incorporated for computing the temporal derivatives in the time average flux approximations. The high-order method is blended with an admissible low-order method at the subcell level to control the Gibbs oscillations and maintain the physical admissibility of the solution. Finally, several test cases involving high Lorentz factors, low densities, low pressures, strong shock waves, and other discontinuities are used to demonstrate the robustness, accuracy, and effectiveness of the proposed method. These simulations are performed with AMR using various linear and curved meshes to show the scheme's efficiency and ability to handle complex geometries.

math.NA↗

arXiv2026

Entropy stable numerical schemes for divergence diminishing Chew, Goldberger & Low equations for plasma flows

Chew, Goldberger & Low (CGL) equations are a set of hyperbolic PDEs with non-conservative products used to model the plasma flows, when the assumption of local thermodynamic equilibrium is not valid, and the pressure tensor is assumed to be rotated by the magnetic field. This results in the pressure tensor, which is described by the two scalar components. As the magnetic field also evolves, controlling the divergence of the magnetic field is important. In this work, we consider the generalized Lagrange multiplier (GLM) technique for the CGL model. The resulting model is referred to as the GLM-CGL system. To make the system suitable for entropy-stable schemes, we reformulate the GLM-CGL system by treating some conservative terms as non-conservative. The resulting system has a non-conservative part that does not affect entropy evolution. We then propose entropy stable numerical methods for the GLM-CGL model. The numerical results for the GLM-CGL system are then compared with the CGL system without the GLM divergence diminishing approach to demonstrate that the GLM approach indeed leads to significant improvement in the magnetic field divergence diminishing.

physics.plasm-ph↗

arXiv2025

Many-body electronic structure in pyrochlore superconductor CsBi2 and spin liquid Pr2Ir2O7

The pyrochlore lattice materials can exhibit geometrical frustration, while the related many-body electronic states remain elusive. In this work, we performed scanning tunneling microscopy measurements on the pyrochlore superconductor CsBi2 and spin liquid Pr2Ir2O7 at 0.3 K. For the first time, we obtained atomically resolved images of their (111) surfaces, revealing a hexagonal lattice or a kagome lattice. Tunneling spectroscopy in CsBi2 reveals a nearly fully opened superconductivity gap. The ratio of 2{\Delta}/kBTC = 4.7 suggests relatively strong coupling superconductivity, as compared with that in kagome superconductors AV3Sb5 (A = K, Rb, Cs). In contrast to the previous study categorizing CsBi2 as a type-I superconductor, the applied magnetic field induces a hexagonal vortex lattice in which each vortex core exhibits an intriguing three-fold symmetry state. In Pr2Ir2O7, we observed a spatially homogeneous Kondo-lattice resonance, which is compared with that in the kagome Kondo-lattice material CsCr6Sb6. We further discover that the Kondo resonance exhibits a spatial modulation with three-fold symmetry, and the applied magnetic field induces a Zeeman splitting of the Kondo resonance with intriguing atomic site dependence. We discuss the relations of these many-body electronic phenomena with the pyrochlore lattice geometry and its charge or spin frustration. Our systematic observations offer atomic-scale insights into the many-body electronic structures of the geometrically frustrated pyrochlore superconductors and spin liquids.

cond-mat.str-el↗

arXiv2025

Physical Constraint Preserving Higher Order Finite Volume Schemes for Divergence-Free Astrophysical MHD and RMHD

Higher order finite volume schemes for magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD) are very valuable because they allow us to carry out astrophysical simulations with very high accuracy. However, astrophysical problems sometimes have unusually large Mach numbers, exceptionally high Lorentz factors and very strong magnetic fields. All these effects cause higher order codes to become brittle and prone to code crashes. In this paper we document physical constraint preserving (PCP) methods for treating numerical MHD and RMHD. While unnecessary for standard problems, for stringent astrophysical problems these methods show their value. We describe higher order methods that allow divergence-free evolution of the magnetic field. We present a novel two-dimensional Riemann solver. This two-dimensional Riemann solver plays a key role in the design of PCP schemes for MHD and RMHD. We present a very simple PCP formulation and show how it is amalgamated with the evolution of face-centered magnetic fields. The methods presented here are time-explicit and do not add much to the computational cost. We show that the methods meet their design accuracies and work well on problems that would otherwise be considered too extreme for typical higher order Godunov methods of the type used in computational astrophysics.

astro-ph.IM↗

arXiv2025

Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State

In the realm of relativistic astrophysics, the ideal equation of state with a constant adiabatic index provides a poor approximation due to its inconsistency with relativistic kinetic theory. However, it is a common practice to use it for relativistic fluid flow equations due to its simplicity. Here we develop a high-order Lax-Wendroff flux reconstruction method on Cartesian grids for solving relativistic hydrodynamics equations with several general equations of state available in the literature. We also study the conversion from conservative to primitive variables, which depends on the equation of state in use, and provide an alternative method of conversion when the existing approach does not succeed. For the admissibility of the solution, we blend the high-order method with a low-order method on sub-cells and prove its physical admissible property in the case of all the equations of state used here. Lastly, we validate the scheme by several test cases having strong discontinuities, large Lorentz factor, and low density or pressure in one and two dimensions.

math.NA↗

arXiv2025

Chew, Goldberger & Low Equations: Eigensystem Analysis and Applications to One-Dimensional Test Problems

Chew, Goldberger & Low (CGL) equations describe one of the simplest plasma flow models that allow anisotropic pressure, i.e., pressure is modeled using a symmetric tensor described by two scalar pressure components, one parallel to the magnetic field, another perpendicular to the magnetic field. The system of equations is a non-conservative hyperbolic system. In this work, we analyze the eigensystem of the CGL equations. We present the eigenvalues and the complete set of right eigenvectors. We also prove the linear degeneracy of some of the characteristic fields. Using the eigensystem for CGL equations, we propose HLL and HLLI Riemann solvers for the CGL system. Furthermore, we present the AFD-WENO schemes up to the seventh order in one dimension and demonstrate the performance of the schemes on several one-dimensional test cases.

math.NA↗

arXiv2025

Second order divergence constraint preserving schemes for two-fluid relativistic plasma flow equations

Two-fluid relativistic plasma flow equations combine the equations of relativistic hydrodynamics with Maxwell's equations for electromagnetic fields, which involve divergence constraints for the magnetic and electric fields. When developing numerical schemes for the model, the divergence constraints are ignored, or Maxwell's equations are reformulated as Perfectly Hyperbolic Maxwell's (PHM) equations by introducing additional equations for correction potentials. In the latter case, the divergence constraints are preserved only as the limiting case. In this article, we present second-order numerical schemes that preserve the divergence constraint for electric and magnetic fields at the discrete level. The schemes are based on using a multidimensional Riemann solver at the vertices of the cells to define the numerical fluxes on the edges. The second-order accuracy is obtained by reconstructing the electromagnetic fields at the corners using a MinMod limiter. The discretization of Maxwell's equations can be combined with any consistent and stable discretization of the fluid parts. In particular, we consider entropy-stable schemes for the fluid part. The resulting schemes are second-order accurate, entropy stable, and preserve the divergence constraints of the electromagnetic fields. We use explicit and IMEX-based time discretizations. We then test these schemes using several one- and two-dimensional test cases. We also compare the divergence constraint errors of the proposed schemes with schemes having no divergence constraints treatment and schemes based on the PHM-based divergence cleaning.

math.NA↗

arXiv2024

Bound Preserving Lax-Wendroff Flux Reconstruction Method for Special Relativistic Hydrodynamics

Lax-Wendroff flux reconstruction (LWFR) schemes have high order of accuracy in both space and time despite having a single internal time step. Here, we design a Jacobian-free LWFR type scheme to solve the special relativistic hydrodynamics equations on Cartesian grids. We then blend the scheme with a first-order finite volume scheme to control the oscillations near discontinuities. We also use a scaling limiter to preserve the physical admissibility of the solution after ensuring the scheme is admissible in means. A particular focus is given to designing a discontinuity indicator model to detect the local non-smoothness in the solution of the highly non-linear relativistic hydrodynamics equations. Finally, we present numerical results for a wide range of test cases to show the robustness and efficiency of the proposed scheme.

math.NA↗

arXiv2024

Second order divergence constraint preserving entropy stable finite difference schemes for ideal two-fluid plasma flow equations

Two-fluid plasma flow equations describe the flow of ions and electrons with different densities, velocities, and pressures. We consider the ideal plasma flow i.e. we ignore viscous, resistive, and collision effects. The resulting system of equations has flux consisting of three independent components, one for ions, one for electrons, and a linear Maxwell's equation flux for the electromagnetic fields. The coupling of these components is via source terms. In this article, we present {conservative} second-order finite difference schemes that ensure the consistent evolution of the divergence constraints on the electric and magnetic fields. The key idea is to design a numerical solver for Maxwell's equations using the multidimensional Riemann solver at the vertices, ensuring discrete divergence constraints; for the fluid parts, we use an entropy-stable discretization. The proposed schemes are co-located, second-order accurate, entropy stable, and ensure divergence-free evolution of the magnetic field. We use explicit and IMplicit-EXplicit (IMEX) schemes for time discretizations. To demonstrate the accuracy, stability, and divergence constraint-preserving ability of the proposed schemes, we present several test cases in one and two dimensions. We also compare the numerical results with those obtained from schemes with no divergence cleaning and those employing perfectly hyperbolic Maxwell (PHM) equations-based divergence cleaning methods for Maxwell's equations.

math.NA↗

arXiv2024

Optical conductivity of the metallic pyrochlore iridate Pr$_2$Ir$_2$O$_7$: Influence of spin-orbit coupling and electronic correlations on the electronic structure

The synergy of strong spin-orbit coupling and electron-electron interactions gives rise to unconventional topological states, such as topological Mott insulator, Weyl semimetal, and quantum spin liquid. In this study, we have grown single crystals of the pyrochlore iridate Pr$_2$Ir$_2$O$_7$ and explored its magnetic, lattice dynamical, and electronic properties. While Raman spectroscopy data reveal six phonon modes confirming the cubic \textit{Fd$\bar{3}$m} crystal symmetry, dc magnetic susceptibility data show no anomalies and hence indicate the absence of magnetic phase transitions down to 2~K. Both temperature-dependent electric transport and optical conductivity data reveal the metallic character of Pr$_2$Ir$_2$O$_7$. The optical conductivity spectrum contains a mid-infrared absorption band, which becomes more pronounced with decreasing temperature due to spectral weight transfer from high to low energies. The presence of the mid-infrared band hints at the importance of correlation physics. The optical response furthermore suggests that Pr$_2$Ir$_2$O$_7$ is close to the Weyl semimetal phase.

cond-mat.str-el↗

arXiv2024

Entropy stable finite difference schemes for Chew, Goldberger & Low anisotropic plasma flow equations

In this article, we consider the Chew, Goldberger \& Low (CGL) plasma flow equations, which is a set of nonlinear, non-conservative hyperbolic PDEs modelling anisotropic plasma flows. These equations incorporate the double adiabatic approximation for the evolution of the pressure, making them very valuable for plasma physics, space physics and astrophysical applications. We first present the entropy analysis for the weak solutions. We then propose entropy-stable finite-difference schemes for the CGL equations. The key idea is to rewrite the CGL equations such that the non-conservative terms do not contribute to the entropy equations. The conservative part of the rewritten equations is very similar to the magnetohydrodynamics (MHD) equations. We then symmetrize the conservative part by following Godunov's symmetrization process for MHD. The resulting equations are then discretized by designing entropy conservative numerical flux and entropy diffusion operator based on the entropy scaled eigenvectors of the conservative part. We then prove the semi-discrete entropy stability of the schemes for CGL equations. The schemes are then tested using several test problems derived from the corresponding MHD test cases.

math.NA↗

arXiv2024

Going Beyond the MHD Approximation: Physics-Based Numerical Solution of the CGL Equations

We present a new numerical model for solving the Chew-Goldberger-Low system of equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and geospace environments are often observed to be in an anisotropic state with distinctly different parallel and perpendicular pressure components. The CGL system represents the simplest leading order correction to the common isotropic MHD model that still allows to incorporate the latter's most desirable features. However, the CGL system presents several numerical challenges: the system is not in conservation form, the source terms are stiff, and unlike MHD it is prone to a loss of hyperbolicity if the parallel and perpendicular pressures become too different. The usual cure is to bring the parallel and perpendicular pressures closer to one another; but that has usually been done in an ad hoc manner. We present a physics-informed method of pressure relaxation based on the idea of pitch-angle scattering that keeps the numerical system hyperbolic and naturally leads to zero anisotropy in the limit of very large plasma beta. Numerical codes based on the CGL equations can, therefore, be made to function robustly for any magnetic field strength, including the limit where the magnetic field approaches zero. The capabilities of our new algorithm are demonstrated using several stringent test problems that provide a comparison of the CGL equations in the weakly and strongly collisional limits. This includes a test problem that mimics interaction of a shock with a magnetospheric environment in 2D.

physics.plasm-ph↗

arXiv2024

Automated Detection of Galactic Rings from SDSS Images

Morphological features in galaxies, like spiral arms, bars, rings, tidal tails etc. carry information about their structure, origin and evolution. It is therefore important to catalog and study such features and to correlate them with other basic galaxy properties, the environment in which the galaxies are located and their interactions with other galaxies. The volume of present and future data on galaxies is so large that traditional methods, which involve expert astronomers identifying morphological features through visual inspection, are no longer sufficient. It is therefore necessary to use AI based techniques like machine learning and deep learning for finding morphological structures quickly and efficiently. We report in this study the application of deep learning for finding ring like structures in galaxy images from the Sloan Digital Sky Survey (SDSS) data release DR18. We use a catalog by Buta (2017) of ringed galaxies from the SDSS to train the network, reaching good accuracy and recall, and generate a catalog of 29420 galaxies of which 4855 have ring like structures with prediction confidence exceeding 90 percent. Using a catalog of barred galaxy images identified by Abraham et. al. (2018) using deep learning techniques, we identify a set of 2087 galaxies with bars as well as rings. The catalog should be very useful in understanding the origin of these important morphological structures. As an example of the usefulness of the catalog, we explore the environments and star formation characteristics of ring galaxies in our sample.

astro-ph.GA↗

arXiv2024

Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws are extremely popular because, for multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume WENO or DG schemes. Such schemes come in two formulations. The very popular classical finite difference WENO (FD-WENO) method (Shu and Osher, J. Comput. Phys., 83 (1989) 32-78) relies two reconstruction steps applied to two split fluxes. However, the method cannot accommodate different types of Riemann solvers and cannot preserve free stream boundary conditions on curvilinear meshes. This limits its utility. The alternative finite difference WENO (AFD-WENO) method can overcome these deficiencies, however, much less work has been done on this method. The reasons are three-fold. First, it is difficult for the casual reader to understand the intricate logic that requires higher order derivatives of the fluxes to be evaluated at zone boundaries. The analytical methods for deriving the update equation for AFD-WENO schemes are somewhat recondite. To overcome that difficulty, we provide an easily accessible script that is based on a computer algebra system in Appendix A of this paper. Second, the method relies on interpolation rather than reconstruction, and WENO interpolation formulae have not been documented in the literature as thoroughly as WENO reconstruction formulae. In this paper, we explicitly provide all necessary WENO interpolation formulae that are needed for implementing AFD-WENO up to ninth order. The third reason is that AFD-WENO requires higher order derivatives of the fluxes to be available at zone boundaries. Since those derivatives are usually obtained by finite differencing the zone-centered fluxes, they become susceptible to a Gibbs phenomenon when the solution ...

math.NA↗

arXiv2024

Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Systems with Non-Conservative Products

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for conservation laws represent a technology that has been reasonably consolidated. They are extremely popular because, when applied to multidimensional problems, they offer high order accuracy at a fraction of the cost of finite volume WENO or DG schemes. They come in two flavors. There is the classical finite difference WENO (FD-WENO) method (Shu and Osher, J. Comput. Phys., 83 (1989) 32-78). However, in recent years there is also an alternative finite difference WENO (AFD-WENO) method which has recently been formalized into a very useful general-purpose algorithm for conservation laws (Balsara et al., Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws, submitted to CAMC (2023)). However, the FD-WENO algorithm has only very recently been formulated for hyperbolic systems with non-conservative products (Balsara et al., Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products, to appear CAMC (2023)). In this paper we show that there are substantial advantages in obtaining an AFD-WENO algorithm for hyperbolic systems with non-conservative products. Such an algorithm is documented in this paper. We present an AFD-WENO formulation in fluctuation form that is carefully engineered to retrieve the flux form when that is warranted and nevertheless extends to non-conservative products. The method is flexible because it allows any Riemann solver to be used. The formulation we arrive at is such that when non-conservative products are absent it reverts exactly to the formulation in the second citation above which is in exact flux conservation form. The ability to transition to a precise conservation form when non-conservative products are absent ensures, via the Lax-Wendroff theorem, that shock locations will be exactly ...

math.NA↗

arXiv2023

Entropy stable discontinuous Galerkin schemes for two-fluid relativistic plasma flow equations

This article proposes entropy stable discontinuous Galerkin schemes (DG) for two-fluid relativistic plasma flow equations. These equations couple the flow of relativistic fluids via electromagnetic quantities evolved using Maxwell's equations. The proposed schemes are based on the Gauss-Lobatto quadrature rule, which has the summation by parts (SBP) property. We exploit the structure of the equations having the flux with three independent parts coupled via nonlinear source terms. We design entropy stable DG schemes for each flux part, coupled with the fact that the source terms do not affect entropy, resulting in an entropy stable scheme for the complete system. The proposed schemes are then tested on various test problems in one and two dimensions to demonstrate their accuracy and stability.

math.NA↗