Discrete Flux Research Articles

T-duality and flavor symmetries in Little String Theories

We explore the T-duality web of 6D Heterotic Little String Theories, focusing on flavor algebra reducing deformations. A careful analysis of the full flavor algebra, including Abelian factors, shows that the flavor rank is preserved under T-duality. This suggests a new T-duality invariant in addition to the Coulomb branch dimension and the two-group structure constants. We also engineer Little String Theories with non-simply laced flavor algebras, whose appearance we attribute to certain discrete 3-form fluxes in M-theory. Geometrically, these theories are engineered in F-theory with non-Kähler favorable K3 fibers. This geometric origin leads us to propose that freezing fluxes are preserved across T-duality. Along the way, we discuss various exotic models, including two inequivalent Spin(32)/ℤ2 models that are dual to the same E8 × E8 theory, and a family of self-T-dual models.

Analysis of natural convection heat transfer in a rectangular cavity with discrete heat flux: Implications for building thermal management using artificial neural networks

This study numerically investigates free convection within a rectangular air-filled cavity, simulating real-romm conditions. The top, bottom, and one sidewall are at constant temperatures, while the opposite sidewall has a constant discrete heat flux, akin to heater appliances. The impact of heating intensity, length, and position on temperature distribution is explored. Artificial Neural Networks (ANN) are utilized to correlate the average Nusselt number, providing a model for engineering applications in building thermal management. The dataset includes 2436 simulation runs with varying parameter: Rayleigh number (103 to 106), aspect ratio (0.5 to 2), heating surface length (0.1 to 1), and elevation (0.05 to 0.95). Results show increased Rayleigh numbers intensify the stream function and promote uniform temperature distribution. The elevation of the heating surface influences temperature distribution, with placement closer to the floor or ceiling optimizing heat transfer. ANN modeling predicts the average Nusselt number with high precision (±3%).

The cell-centered positivity-preserving finite volume scheme for 3D convection–diffusion equation on distorted meshes

PurposeThis paper aims to construct positivity-preserving finite volume schemes for the three-dimensional convection–diffusion equation that are applicable to arbitrary polyhedral grids.Design/methodology/approachThe cell vertices are used to define the auxiliary unknowns, and the primary unknowns are defined at cell centers. The diffusion flux is discretized by the classical nonlinear two-point flux approximation. To ensure the fully discrete scheme has positivity-preserving property, an improved discretization method for the convection flux was presented. Besides, a new positivity-preserving vertex interpolation method is derived from the linear reconstruction in the discretization of convection flux. Moreover, the Picard iteration method may have slow convergence in solving the nonlinear system. Thus, the Anderson acceleration of Picard iteration method is used to solve the nonlinear system. A condition number monitor of matrix is employed in the Anderson acceleration method to achieve better robustness.FindingsThe new scheme is applicable to arbitrary polyhedral grids and has a second-order accuracy. The results of numerical experiments also confirm the positivity-preserving of the discretization scheme.Originality/value1. This article presents a new positivity-preserving finite volume scheme for the 3D convection–diffusion equation. 2. The new discretization scheme of convection flux is constructed. 3. A new second-order interpolation algorithm is given to eliminate the auxiliary unknowns in flux expressions. 4. An improved Anderson acceleration method is applied to accelerate the convergence of Picard iterations. 5. This scheme can solve the convection–diffusion equation on the distorted meshes with second-order accuracy.

Magnetohydrodynamic mixed convection of nanofluid within an annular space filled partially with a porous layer between a lid-driven wall and a discrete heater

Heat and mass transfer inside a partially porous medium is a complex coupling process in which the interface boundary conditions between free and porous space are critical for a wide range of engineering applications, including natural and engineered fractures in oil and gas extraction. In this study, we looked into the numerical simulation of magnetohydrodynamic mixed convection of nanofluid in an annular partially porous space between two coaxial cylinders with a permeable interface, in which we investigated the contribution of the interface in order to better understand the heat transfer processes. The inner cylinder is subjected to a discrete uniform heat flux, while the external cylinder is kept at a uniform cold temperature and moving at a constant speed. The base walls are designed to be impermeable and insulated. A finite difference-based vorticity-stream function method is used to solve the nonlinear coupled conservation equations using the Successive Over Relaxation approach (SOR). The acquired numerical results in terms of streamlines, isotherms, and Nusselt numbers are shown to demonstrate the effect of various control factors such as the Rayleigh number, Darcy number, Hartmann number, Reynold number, nanoparticle concentration, and the direction of the outer wall. The results of this numerical simulation show that the upward or downward direction of the wall under these control factors plays an important role in improving the rate of heat transfer or replacing the magnetic effect by limiting and controlling heat transfer

A Conservative Solid-Gas Coupling Scheme with Overlapping Meshes for Combustion Simulation of Propellants with Voids

ABSTRACT A conservative coupling scheme with overlapping meshes for the combustion simulation of propellants with voids is established. The two main ingredients of this scheme are the conservative calculation of fluxes of mass, momentum, energy, and species and the robust treatment of voids. Specifically, for the discrete flux calculation, firstly the solid-gas interfaces are captured by the level-set method and then sampling points are generated between the interfaces at consecutive time steps, and these points are used to ensure the conservation of these quantities up to each grid of the gas domain. For the second ingredient, the void before exposure is treated as “solid” with properties of the air. Once an exposure condition is met, the topological change of the void is realized by reinitializing the level set function inside and on the boundary of the void. Overall, the scheme is conservative and robust, which is validated with experimental results.

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

We extend the monolithic convex limiting (MCL) methodology to nodal discontinuous Galerkin spectral-element methods (DGSEMS). The use of Legendre-Gauss-Lobatto (LGL) quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes. Compared to many other continuous and discontinuous Galerkin method variants, a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcell flux discretization. Representing a high-order spatial semi-discretization in terms of intermediate states, we perform flux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains. In addition, local bounds may be imposed on scalar quantities of interest. In contrast to limiting approaches based on predictor-corrector algorithms, our MCL procedure for LGL-DGSEM yields nonlinear flux approximations that are independent of the time-step size and can be further modified to enforce entropy stability. To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations, we run simulations for challenging setups featuring strong shocks, steep density gradients, and vortex dominated flows.

A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme

We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution towards the unique entropy solution by first estimating the supremum norm and the total variation of the discrete solution, and second by constructing a discrete kinetic entropy-entropy flux pair being given a continuous entropy-entropy flux pair of the hyperbolic system. We finally illustrate our results with numerical simulations of the advection equation and the Burgers equation.

Direct Field-Oriented Control of Induction Motor with Discrete Full-Order Flux Observer

Direct Field-Oriented Control of Induction Motor with Discrete Full-Order Flux Observer

New non-supersymmetric flux vacua in string theory

In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in [1] for which we provide the first explicit examples in Calabi-Yau orientifold compactifications with discrete fluxes below their respective tadpole constraint. As a proof of concept, we study the degree 18 hypersurface in weighted projective space CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{CP} $$\\end{document}1,1,1,6,9. Furthermore, we look at 10 additional orientifolds with h1,2 = 2, 3. We find several flux vacua with hierarchical suppression of the vacuum energy with respect to the gravitino mass. These solutions provide a crucial stepping stone for the construction of explicit de Sitter vacua in string theory. Lastly, we also report the difference in the distribution of W0 between supersymmetric and non-supersymmetric minima.

Importance of satisfying thermodynamic consistency in optoelectronic device simulations for high carrier densities

We show the importance of using a thermodynamically consistent flux discretization when describing drift–diffusion processes within light emitting diode simulations. Using the classical Scharfetter–Gummel scheme with Fermi–Dirac statistics is an example of such an inconsistent scheme. In this case, for an (In,Ga)N multi quantum well device, the Fermi levels show an unphysical hump within the quantum well regions. This result originates from neglecting diffusion enhancement associated with Fermi–Dirac statistics in the numerical flux approximation. For a thermodynamically consistent scheme, such as the SEDAN scheme, the humps in the Fermi levels disappear. We show that thermodynamic inconsistency has far reaching implications on the current–voltage curves and recombination rates.

Noninvertible anomalies in SU(N) × U(1) gauge theories

We study 4-dimensional SU(N) × U(1) gauge theories with a single massless Dirac fermion in the 2-index symmetric/antisymmetric representations and show that they are endowed with a noninvertible 0-form {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} chiral symmetry along with a 1-form {mathbb{Z}}_N^{(1)} center symmetry. By using the Hamiltonian formalism and putting the theory on a spatial three-torus mathbbm{T} 3, we construct the non-unitary gauge invariant operator corresponding to {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} and find that it acts nontrivially in sectors of the Hilbert space characterized by selected magnetic fluxes. When we subject mathbbm{T} 3 to {mathbb{Z}}_N^{(1)} twists, for N even, in selected magnetic flux sectors, the algebra of {overset{sim }{mathbb{Z}}}_{2left(Npm 2right)}^{upchi} and {mathbb{Z}}_N^{(1)} fails to commute by a ℤ2 phase. We interpret this noncommutativity as a mixed anomaly between the noninvertible and the 1-form symmetries. The anomaly implies that all states in the torus Hilbert space with the selected magnetic fluxes exhibit a two-fold degeneracy for arbitrary mathbbm{T} 3 size. The degenerate states are labeled by discrete electric fluxes and are characterized by nonzero expectation values of condensates. In an appendix, we also discuss how to construct the corresponding noninvertible defect via the “half-space gauging” of a discrete one-form magnetic symmetry.

Numerical Treatment of State‐Dependent Permeability in Multiphysics Problems

AbstractConstitutive laws relating fluid potentials and fluxes in a nonlinear manner are common in several porous media applications, including biological and reactive flows, poromechanics, and fracture deformation. Compared to the standard, linear Darcy's law, such enhanced flux relations increase both the degree of nonlinearity, and, in the case of multiphysics simulations, coupling strength between processes. While incorporating the nonlinearities into simulation models is thus paramount for computational efficiency, correct linearization, as is needed for incorporation in Newton's method, is challenging from a practical perspective. The standard approach is therefore to ignore nonlinearities in the permeability during linearization. For finite volume methods, which are popular in porous media applications, complete linearization is feasible only for the simplest flux discretization, namely the two‐point flux approximation. We introduce an approximated linearization scheme for finite volume methods that is exact for the two‐point scheme and can be applied to more advanced and accurate discretizations, exemplified herein by a multi‐point flux stencil. We test the new method for both nonlinear porous media flow and several multiphysics simulations. Our results show that the new linearization consistently outperforms the standard approach. Moreover our scheme achieves asymptotic second order convergence of the Newton iterations, in contrast to the linear convergence obtained with the standard approach.

A nonlinear scheme preserving maximum principle for heterogeneous anisotropic diffusion equation

We present a new nonlinear method in order to preserve the maximum principle for the diffusion problem with heterogeneous anisotropic coefficient. It is well-known that for diffusion problems with general discontinuous coefficients, the existing cell-centered finite volume schemes on general meshes cannot unconditionally satisfy the discrete maximum principle (DMP), i.e., there are always certain severe restrictions on the mesh-cell geometry or locations of discontinuity in order to preserve DMP. To deal with the issue we propose a nonlinear method of modifying discrete flux of linear second-order schemes into a new conservative flux. Then the resulting scheme keeps conservation and accuracy, and has the structure preserving maximum principle without imposing those severe restrictions. Specifically, we will start with the diamond scheme whose flux is linear and has second-order accuracy, but has no the structure preserving maximum principle. Then the nonlinear correction method is applied to get a scheme satisfying the discrete maximum principle unconditionally. We give some theoretical analysis including the coercivity property and a prior estimation. Numerical results show that the accuracy of our new scheme is superior to the existing scheme preserving maximum principle, and in some cases the accuracy can even be improved by one order of magnitude.

Can strong substorm-associated MeV electron injections be an important cause of large radiation belt enhancements?

It has become well-established that strong outer radiation belt enhancements are due to wave-driven electron energization by whistler-mode chorus waves. However, in this study, we examine strong MeV electron injections on 10 July 2019 and find substantial evidence that such injections may be a crucial contributor to outer radiation belt enhancement events. For such an examination, it is essential to precisely separate temporal flux changes from spatial variations observed as Van Allen Probes move along their orbits. Employing a new “hourly snapshot” analysis approach, we discover unprecedented details of electron flux evolutions that suggest that for this event, the outer belt enhancement was not continuous but instead intermittent, mostly composed of 4 large discrete injection-driven flux increases. The injections appear as sharp flux increases when observed near apogee. Otherwise, by comparing hourly snapshots for different times, we infer injections and infer temporally stable fluxes between injections, despite strong and continuous chorus emission. The fast and intermittent electron flux growth successively extending earthwards implies cumulative outer belt enhancement via a series of repetitive inward transport associated with injection-induced electric fields.

High-order implicit RBF-based differential quadrature-finite volume method on unstructured grids: Application to inviscid and viscous compressible flows

This paper exploits the potential of a high-order implicit radial basis function-based differential quadrature-finite volume (IRBFDQ-FV) method for effective simulation of inviscid and viscous compressible flows using unstructured grids. The framework of IRBFDQ-FV method is based on finite volume discretization which can guarantee conservation of mass, momentum and energy. The flow field variables within each control cell are represented by a fourth-order approximation constructed by a Taylor series expansion to the cell center with spatial derivatives as the undetermined coefficients. All spatial derivatives are computed by the meshless and highly converged RBF-based differential quadrature (RBFDQ) technique. Regarding flux evaluation, the discrete gas-kinetic flux solver is applied to evaluate inviscid and viscous fluxes simultaneously for compressible viscous flows. Resultantly, the special mathematical treatment for the viscous flux, which is usually adopted in other high-order methods, can be avoided. A point extrema-based extended bounds (PEEB) shock-capturing limiter is introduced to eliminate spurious numerical oscillations near discontinuities. Due to the implicit nature of the proposed method, implicit time-stepping schemes compatible with the spatial accuracy are devised to efficiently solve the resulting discretized equations. Representative compressible flow problems are simulated to verify the high-order accuracy, excellent efficiency and robustness of the present method. Comparison with two other high-order finite volume methods further shows competitiveness of the present method in solving compressible flow problems on unstructured grids.

On the role of spectral properties of viscous flux discretization for flow simulations on marginally resolved grids

In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier–Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different classes, with poor and better representation of spectral properties at high wavenumbers. Both theoretical and numerical results have revealed that the method with better properties at high wavenumbers, denoted as α-damping type discretization, produced superior solutions compared to the other class of methods. The proposed compact α-damping method converged towards the direct numerical simulation (DNS) solution at lower grid resolution compared with the other class of methods and is, therefore, a better candidate for high fidelity large-eddy simulations (LES) and DNS studies.

Gradient based reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows

This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier–Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of derivatives. The higher-order accurate gradients of the velocity components are reused to compute the viscous fluxes for efficiency and significantly improve the solution and gradient quality, as demonstrated by several viscous-flow test cases. The viscous schemes are fourth-order accurate and carefully designed with a high-frequency damping property, which has been identified as a critically important property for stable compressible-flow simulations with shock waves (Chamarthi et al., 2022). Shocks and material discontinuities are captured using a monotonicity-preserving (MP) scheme, which is also improved by reusing the gradients. For inviscid test cases, The proposed scheme is fourth-order for linear and second-order accurate for non-linear problems. Several numerical results obtained for simulations of complex viscous flows are presented to demonstrate the accuracy and robustness of the proposed methodology.

Numerical Analysis of High Speed Flow Applications using Various Flux Schemes

Numerical analysis using computational fluid dynamics is an affordable and effective method with increasing relevance every day in research and engineering problems. Choosing an appropriate convective discretization scheme is paramount importance for obtaining more accurate solutions using CFD methods. The present study compares two commonly used numerical convective schemes, the upwind scheme of Advection Upstream Splitting Method (AUSM) and the central schemes of Kurganov-Noelle-Petrova and Kurganov-Tadmor scheme (K-T) have been made to find the better central scheme. These two schemes are validated with inviscid 1D and 2D problems such as Sod’s shock tube, forward facing step in a Mach 3 tunnel, 15 Degree ramp in a Mach 2 supersonic tunnel, the Mach-reflection problem and scramjet engine operating under high Mach number. The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. Comparison of results obtained by these 2 schemes is presented using density contours and surface property changes. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions.
 HIGHLIGHTS
 
 This paper focuses on two convective flux discretization techniques i.e. the upwind scheme of AUSM and the central schemes of K-T and KNP
 Inviscid simulations for various problems in the supersonic as well as hypersonic regime were used in Sod’s 1-Dimensional Shock Tube, flow over forward facing step in supersonic wind tunnel and Mach 5 flow thorough scramjet engine
 The AUSM and K-T schemes are robust enough to capture all the features of compressible flows. It has been observed that both the schemes are robust enough to capture the flow features of the problems and that they have better accuracy for different conditions
 
 GRAPHICAL ABSTRACT

Linear discrete velocity model-based lattice Boltzmann flux solver for simulating acoustic propagation in fluids.

A linear lattice velocity model is developed, and a corresponding lattice Boltzmann flux solver (LBFS) is constructed based on it. This solver calculates the fluxes of the linearized Euler equations (LEEs), which are discretized by the finite volume method (FVM), and can simulate acoustic propagation in fluids. First, the expressions for the distribution function and the lattice velocity of the linear discrete velocity model are constructed using the moment relations in linear form. Second, based on Chapman-Enskog analysis and moment relations, the mesoscopic flux expression can be constructed by comparing the linear lattice Boltzmann equation and LEEs. Finally, the developed scheme is used to calculate the LEE flux term. The developed linear lattice velocity model-based LBFS has the following advantages: (i) It extends the lattice Boltzmann model-based flux solver from solving the macroscopic equations of fluid dynamics to solving linear equations; (ii) it also inherits the advantages of the Boltzmann model-type flux solver. The variables at the interface are calculated from the local solution of the lattice Boltzmann equation, making it more physical. In addition, least-squares-based finite differences and Gaussian integration are used for the FVM to discretize the LEE, making it a high-precision algorithm. Thus, the developed algorithm can accurately capture acoustic propagation in fluids and acoustic scattering in complex geometries. Several numerical cases for propagating acoustics in fluids are simulated to validate the accuracy and robustness of the present algorithm, and an accuracy test shows it approaches fourth-order accuracy.

Energy-conserving formulation of the two-fluid model for incompressible two-phase flow in channels and pipes

We show that the one-dimensional (1D) two-fluid model (TFM) for stratified flow in channels and pipes (in its incompressible, isothermal form) satisfies an energy conservation equation, which arises naturally from the mass and momentum conservation equations that constitute the model. This result extends upon earlier work on the shallow water equations (SWE), with the important difference that we include non-conservative pressure terms in the analysis, and that we propose a formulation that holds for ducts with an arbitrary cross-sectional shape, with the 2D channel and circular pipe geometries as special cases.The second novel result of this work is the formulation of a finite volume scheme for the TFM that satisfies a discrete form of the continuous energy equation. This discretization is derived in a manner that runs parallel to the continuous analysis. Due to the non-conservative pressure terms it is essential to employ a staggered grid, which requires careful consideration in defining the discrete energy and energy fluxes, and the relations between them and the discrete model. Numerical simulations confirm that the discrete energy is conserved.