A new targeted essentially non-oscillatory (TENO) limiter with adaptive dissipation has been developed for the 3rd- and 4th-order spectral difference method. This limiter can potentially be useful ...for other nodal-based discontinuous high-order methods as well. Unlike traditional WENO limiters for these methods which limit low-order moments one by one, the new limiter is based on a direct convex combination of reconstruction polynomial candidates. This strategy ensures the good computational efficiency for high order reconstructions. The reconstruction stencils only involve nodal values from the target cell and its neighbors sharing faces with it. The reconstruction employs Hermite polynomials, making the new limiter compact. It can be implemented in a dimension-by-dimension manner for multi-dimensional problems, which is consistent with the spectral difference method. To further enhance efficiency, a TENO-based troubled-cell indicator is also developed to only activate limiters in troubled cells. Extensive one-dimensional and two-dimensional numerical experiments validate the performance of the new TENO-based limiter and indicator. In summary, the limiter is much less dissipative than WENO limiters and can resolve richer small-scale flow structures on coarse meshes. The indicator precisely marks out troubled cells, slightly improving over the KXRCF indicator.
The Working Mind Pascual-Leone, Juan; Johnson, Janice M
2021, 2021-04-13
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A general organismic-causal theory that explicates working memory and executive function developmentally, clarifying the nature of human intelligence. In The Working Mind, Juan Pascual-Leone and ...Janice M. Johnson propose a general organismic-causal theory that explicates working memory and executive function developmentally and by doing so clarifies the nature of human intelligence. Pascual-Leone and Johnson explain “from within” (that is, from a subject's own processing perspective) cognitive developmental stages of growth, describing key causal factors that can account for the emergence of the working mind as a functional totality. Among these factors is a maturationally growing mental attention. After reviewing meaning-driven processes and constructivist knowledge principles that underlie what Pascual-Leone and Johnson term their Theory of Constructive Operators (TCO), they propose the TCO as as a developmental and neuropsychological approach to human cognitive and affective processes and their development. They present a novel method of mental task analysis that generates from-within process models of subjects' attempts to solve specific tasks. They provide an interpretation of brain semiotic processes that deploys TCO in functionally distinct brain locations. Finally, they show how TCO explicates complex human issues including consciousness, the self, the will, motivation, and individual differences, with applications in education, psychotherapy, and cognitive neuropsychology.
In Fu et al. (2016), a family of high-order TENO shock-capturing schemes has been proposed for compressible fluid simulations within a finite-difference framework. With the TENO weighting strategy, ...each candidate stencil is either applied for the final reconstruction with its optimal weight or discarded completely when crossed by discontinuities. In this paper, with the observation that the local flow scales can be judged to be smooth or non-smooth explicitly, we propose a novel low-dissipation finite-volume method based on a new TENO reconstruction. Firstly, a new ENO-like stencil selection paradigm, which adapts between three three-point small stencils and a large candidate stencil, is proposed. The resulting TENO scheme inherits the low-dissipation advantage of original TENO schemes and can be extended to arbitrarily high-order reconstruction without significant complexity increase. The optimal background linear scheme on the three small stencils and that on the large stencil can be optimized either approaching high-order accuracy or better spectral properties separately. Secondly, within the finite-volume framework, a “low-dissipation” Riemann solver is applied for flux computing when the large candidate stencils for both the left- and right-side reconstruction are judged as smooth whereas a robust ”dissipative” Riemann solver is adopted when one large candidate stencil crosses discontinuities. Since the numerical dissipation from both the reconstruction stage and the flux computing stage can be tuned according to the TENO weighting strategy, the proposed finite-volume method is less-dissipative and provides additional flexibility to handle challenging simulations. A set of benchmark cases is simulated to assess the performance of proposed method.
In this paper, we introduce a novel non-linear uniform subdivision scheme for the generation of curves in Rn, n≥2. This scheme is distinguished by its capacity to reproduce second-degree polynomial ...data on non-uniform grids without necessitating prior knowledge of the grid specificities. Our approach exploits the potential of annihilation operators to infer the underlying grid, thereby obviating the need for end-users to specify such information. We define the scheme in a non-stationary manner, ensuring that it progressively approaches a classical linear scheme as the iteration number increases, all while preserving its polynomial reproduction capability.
The convergence is established through two distinct theoretical methods. Firstly, we propose a new class of schemes, including ours, for which we establish C1 convergence by combining results from the analysis of quasilinear schemes and asymptotically equivalent linear non-uniform non-stationary schemes. Secondly, we adapt conventional analytical tools for non-linear schemes to the non-stationary case, allowing us to again conclude the convergence of the proposed class of schemes.
We show its practical usefulness through numerical examples, showing that the generated curves are curvature continuous.
Information-centric networking (ICN) is being realized as a promising approach to accomplish the shortcomings of current Internet protocol-address-based networking. ICN models are based on naming the ...content to get rid of address-space scarcity, accessing the content via name-based-routing, and caching the content at intermediate nodes to provide reliable, efficient data delivery, and self-certifying contents to ensure better security. Obvious benefits of ICN in terms of fast and efficient data delivery and improved reliability raises ICN as highly promising networking model for Internet of Things (IoT) like environments. IoT aims to connect anyone and/or anything at any time by any path on any place. From last decade, IoT attracts both industry and research communities. IoT is an emerging research field and still in its infancy. Thus, this paper presents the potential of ICN for IoT by providing state-of-the-art literature survey. We discuss briefly the feasibility of ICN features and their models (and architectures) in the context of IoT. Subsequently, we present a comprehensive survey on ICN-based caching, naming, security, and mobility approaches for IoT with appropriate classification. Furthermore, we present operating systems and simulation tools for ICN-IoT. Finally, we provide important research challenges and issues faced by ICN for IoT.
We propose a family of simple second order accurate schemes for the numerical solution of Euler equation of gas dynamics that are (linearly) implicit in the acoustic waves, eliminating the acoustic ...CFL restriction on the time step. The general idea is that explicit differential operators in space relative to convective or material speeds are discretised by upwind schemes or local Lax-Friedrics fluxes and the linear implicit operators, pertaining to acoustic waves, are discretised by central differences. We have compared the results of such schemes on a series of one and two dimensional test problems including classical shock tube configurations. Also we have considered low-Mach number acoustic wave propagation tests as well as nozzle flows in various Mach regimes. The results show that these schemes do not introduce excessive numerical dissipation at low Mach number providing an accurate solution in such regimes. They perform reasonably well also when the Mach number are not too small.
•Second order all-Mach number shock capturing schemes for Euler equations are introduced.•They are based on finite volume discretisation on collocated grid and IMEX methods in time.•Material waves are treated explicitly by upwind or local Lax-Friedrichs fluxes.•Acoustic waves are treated by linearly implicit scheme and central discretisation in space.•The schemes are compared on many 1D and 2D tests in order to identity the most versatile ones.
For solving time-dependent convection-dominated partial differential equations (PDEs), which arise frequently in computational physics, high order numerical methods, including finite difference, ...finite volume, finite element and spectral methods, have been undergoing rapid developments over the past decades. In this article we give a brief survey of two selected classes of high order methods, namely the weighted essentially non-oscillatory (WENO) finite difference and finite volume schemes and discontinuous Galerkin (DG) finite element methods, emphasizing several of their recent developments: bound-preserving limiters for DG, finite volume and finite difference schemes, which address issues in robustness and accuracy; WENO limiters for DG methods, which address issues in non-oscillatory performance when there are strong shocks, and inverse Lax–Wendroff type boundary treatments for finite difference schemes, which address issues in solving complex geometry problems using Cartesian meshes.
We develop fifth-order A-WENO finite-difference schemes based on the path-conservative central-upwind method for nonconservative one- and two-dimensional hyperbolic systems of nonlinear PDEs. The ...main challenges in development of accurate and robust numerical methods for the studied systems come from the presence of nonconservative products. Semi-discrete second-order finite-volume path-conservative central-upwind (PCCU) schemes recently proposed in Castro Díaz et al. (2019) 8 provide one with a reliable Riemann-problem-solver-free numerical method for nonconservative hyperbolic system. In this paper, we extend the PCCU schemes to the fifth-order of accuracy in the framework of A-WENO finite-difference schemes.
We apply the developed schemes to the two-layer shallow water equations. We ensure that the developed schemes are well-balanced in the sense that they are capable of exactly preserving “lake-at-rest” steady states. We illustrate the performance of the new fifth-order schemes on a number of one- and two-dimensional examples, where one can clearly see that the proposed fifth-order schemes clearly outperform their second-order counterparts.
•The proposed fifth-order A-WENO schemes for nonconservative nonlinear hyperbolic systems are robust and highly accurate.•The new schemes have been implemented for the one- and two-dimensional two-layer shallow water equations.•A well-balanced property has been achieved using equivalent reformulations in terms of the equilibria variables.•Numerical examples demonstrate that the proposed schemes clearly outperform their second-order finite-volume counterparts.
•Implicit large eddy simulation of compressible turbulence is performed with newly proposed PnTm-BVD schemes.•More accurate predictions of the turbulence evolution are obtained compared with WENO ...schemes.•Faithful solutions to capture discontinuities are realized with BVD algorithm.•The superiority of PnTm-BVD is more notable in high wave-number region.
Implicit large eddy simulation (ILES) of compressible turbulence with shock capturing schemes requires wide investigations and numerical experiments. In this study, a newly proposed PnTm−BVD (polynomial of n-degree and THINC function of m-level reconstruction based on BVD algorithm) shock capturing scheme is introduced to simulate compressible turbulence flow with ILES. The new scheme is designed by employing high-order linear-weight polynomials and THINC (Tangent of Hyperbola for INterface Capturing) functions with adaptive steepness as the reconstruction candidates. The final reconstruction function in each cell is determined with a multi-stage BVD (Boundary Variation Diminishing) algorithm so as to effectively control numerical oscillation and dissipation. Numerical tests involving shock waves and broadband turbulence are conducted in comparison with WENO (Weighted Essentially Non-oscillatory) schemes which are widely used in ILES. The results demonstrate performing ILES with PnTm−BVD scheme is able to obtain higher resolution and more faithful results than WENO does. Importantly, the superiority of PnTm−BVD becomes more notable in high wave-number region. Thus this paper provides and verifies a new scheme which is promising in providing high-resolution results for real-case ILES of compressible turbulence flow.
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