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A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

The purpose of this study is to investigate the accuracy and applicability of the Flowfield Dependent Variation (FDV) method for large-eddy simulations (LES) of decaying isotropic turbulence.

In an earlier paper, the FDV method was successfully demonstrated for simulations of laminar flows with speeds varying from low subsonic to high supersonic Mach numbers. In the current study, the FDV method, implemented in a finite element framework, is used to perform LESs of decaying isotropic turbulence. The FDV method is fundamentally derived from the Lax–Wendroff Scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the inherent numerical dissipation of FDV contribute to the scheme’s numerical stability and monotonicity. Understanding the role of numerical dissipation that is inherent to the FDV method is essential for the maturation of FDV into a robust scheme for LES of turbulent flows. Accordingly, three types of LES of decaying isotropic turbulence were performed. The first two types of LES utilized explicit subgrid scale (SGS) models, namely, the constant-coefficient Smagorinsky and dynamic Smagorinsky models. In the third, no explicit SGS model was employed; instead, the numerical dissipation inherent to FDV was used to emulate the role played by explicit SGS models. Such an approach is commonly known as Implicit LES (ILES). A new formulation was also developed for quantifying the FDV numerical viscosity that principally arises from the convective terms of the filtered Navier–Stokes equations.

The temporal variation of the turbulent kinetic energy and enstrophy and the energy spectra are presented and analyzed. At all grid resolutions, the temporal profiles of kinetic energy showed good agreement with t^(−1.43) theoretical scaling in the fully developed turbulent flow regime, where t represents time. The energy spectra also showed reasonable agreement with the Kolmogorov’s k^(−5/3) power law in the inertial subrange, with the spectra moving closer to the Kolmogorov scaling at higher-grid resolutions. The intrinsic numerical viscosity and the dissipation rate of the FDV scheme are quantified, both in physical and spectral spaces, and compared with those of the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of the Streamline Upwind/Petrov–Galerkin (SUPG) finite element method are compared. In the initial stages of turbulence development, all three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. It was also observed that the SUPG method is significantly more dissipative than the three LES approaches.

Just as any computational method, the limitations are based on the available computational resources.

Solving problems involving turbulent flows is by far the biggest challenge facing engineers and scientists in the twenty-first century, this is the road that the authors have embarked upon in this paper and the road ahead of is very long.

Understanding turbulence is a very lofty goal and a challenging one as well; however, if the authors succeed, the rewards are limitless.

The derivation of an explicit expression for the numerical viscosity tensor of FDV is an important contribution of this study, and is a crucial step forward in elucidating the fundamental properties of the FDV method. The comparison of viscosities for the three LES cases and the SUPG method has important implications for the application of ILES approach for turbulent flow simulations.

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.

Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.

At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.

The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.

To evaluate the performance of different subgrid kinetic energy models across a range of Reynolds numbers while keeping the grid constant.

A dynamic subgrid kinetic energy model, a static coefficient kinetic energy model, and a “no‐model” method are compared with direct numerical simulation (DNS) data at two friction Reynolds numbers of 180 and 590 for turbulent channel flow.

Results indicate that, at lower Reynolds numbers, the dynamic model more closely matches DNS data. As the amount of energy in the unresolved scales increases, the performance of both kinetic energy models is seen to decrease.

This paper provides guidance to engineers who routinely use a single grid to study a wide range of flow conditions (i.e. Reynolds numbers), and what level of accuracy can be expected by using kinetic energy models for large eddy simulations.

Sequel to the results of the preceding chapter that depicted positive associations of credit with the indicators of growth and development, the present chapter aims at investigating the interrelationships of credit with GDP and HDI separately in a bivariate framework for the selected countries for the period 1990–2019. For this purpose, this chapter first develops a theoretical model in line with the Barro (1991) model where bank credit is introduced as a good institutional component of endogenous growth. Then, it goes for a time series exercise to establish the long-run relations and short-run dynamics for the pairs of variables, credit-GDP and credit-HDI, to justify the linkages between the financial sector and the real sector. The study arrives at mixed results across the countries. In many cases, credit has been identified to be strongly related to income and development indicators in the long run through cointegrated stable relationships. Furthermore, credit makes a causal influence on GDP and HDI in some developed countries whereas GDP becomes a causal factor to credit in some developing countries. It is thus recommended for further aggravation of the two sectors’ linkages under the patronisations of the governments and the monetary authorities of the countries to have high growth of income and development so that a part of the sustainable development goal can be achieved through the financial sector.

Background: Insurance was discovered many centuries before Christ (BC). In the second and third millennia BC, Chinese and Babylonian traders traded risks. Insurance is now the backbone of the economy, but penetration is low in developing countries. Big data, internet of things (IoT), and InsurTech have recently ushered in the fourth industrial revolution in insurance.

Objective: This study examines the Indian challenges and solutions of using Big Data Analytics (BDA).

methodology: A SLR was used to extract themes/variables related to challenges and solutions in adopting BDA in the Indian insurance sector. Google Scholar was searched for relevant literature using keywords. Inclusion and exclusion criteria were used to filter the studies.

Findings: This study identified several barriers to BDA adoption in the Indian insurance industry. Policymakers could use the suggestions to improve insurance service delivery.

Practical implication: Insurers can understand the challenges, and accordingly, they can adopt the proposed solution in this study to enhance the insurance penetration in India.

Financial inclusion is more than just granting access to financial services; it involves fostering individuals’ overall financial health and prosperity. Financial inclusion has gained significant importance for policymakers and academia in the preceding two decades. It encourages individuals by extending ownership of their financial situation and empowering them to make well-informed decisions regarding their future. The literary work highlights the importance of financial inclusion in promoting prosperity and progress in society. Furthermore, the psychological effects of financial inclusion are addressed with an emphasis on reducing anxiety and stress associated with accessing necessary financial resources and increasing experiences of financial assurance and trust. Finally, the current condition of financial inclusion and ongoing initiatives to improve it is discussed with a regional focus on Asia. The idea of the empowered consumer is introduced, along with a discussion of how financial inclusion may enlighten customers, making them more knowledgeable and engaged members of the financial market. Finally, the conclusion presents a global perspective of underdeveloped nations, emphasizing the imperative requirement for financial integration in these places and the potential benefits it can provide. The chapter provides a comprehensive understanding of financial inclusion, its significance, and its psychological effects on people and their communities, particularly in Asia and developing nations.

This article provides a systematic literature review on financial inclusion, offering a comprehensive overview of research publications. It also develops a conceptual framework to outline future research objectives, enhancing understanding and identifying key areas for further investigation.

The data extraction concentrates on facts and figures about financial inclusion from 2005 to 2024. Using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), the study reviews and synthesizes insights from 115 pertinent articles published in 77 high-ranked journals, indexed across three academic databases: Scopus, Web of Science (WoS) and the Australian Business Deans Council (ABDC).

Previous research on financial inclusion demonstrates that out of 115 articles, 50 were published between 2020 and 2024 and 43 between 2015 and 2019. This indicates the increasing trend of research on financial inclusion. Another interesting point is that researchers mostly use regression techniques to analyze the relationship between variables. Notably, reviewing the selected literature is valuable for researchers and practitioners interested in financial inclusion. It synthesizes the existing knowledge on the topic, identifies research gaps and suggests a conceptual framework to direct future studies.

This unique study contributes original value to the financial inclusion literature through a systematic literature review. By synthesizing existing knowledge and identifying research gaps, it presents a novel framework that offers new perspectives and highlights areas for future research, advancing the understanding of financial inclusion.