Finite Difference Technique Research Articles

Photonic hook shaping achieved by the micro-nano fiber array based Janus cylindrical metalens

Abstract Near-field focusing of an electromagnetic wave on the assembly of hexagonally asymmetric arranged close-contact nanofibers into a cylindrical Janus metalens is considered for different fiber sizes and optical properties. We propose combining the meta-material concept with a photonic hook based on the finite-difference time-domain technique. Simulation results show that the cylindrical meta-photonic Janus structure produces the focal region of enhanced optical intensity, which exists in the spatial form of a localized structured light known as a photonic hook. A detailed study of all key parameters of a photonic hook depending on the Janus metalens topology and optical properties of the fiber filling is carried out. The structure conditions have been determined for the beam waist of a photonic hook that is less than the diffraction limit. This Janus cylindrical metalens may contribute to the versatile control of photonic hook generation in the applications of bio-photonics and optical microscopes.

Flowing Liquid Crystal Torons Around Obstacles

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Analysis of thermophoretic and Brownian diffusions in hydromagnetic curvilinear flow of Carreau nanofluid with activation energy and heat generation

This study presents a theoretical analysis of the thermophoretic and Brownian diffusion effects on the magnetized flow of Carreau nanofluid over a stretchable curved surface. The investigation includes the impact of heat generation and activation energy, which are incorporated into the energy and concentration equations, respectively. The mathematical model of the boundary layer flow is formulated as a set of nonlinear partial differential equations using curvilinear coordinates. These equations are transformed into ordinary differential equations through the application of appropriate similarity variables. The resulting system is solved numerically by using the shooting method along with the Runge-Kutta technique. The accuracy of the numerical results is further verified by the Keller-box method, a finite difference technique. The obtained results are also checked by giving a comparison table with the published data in the literature. Furthermore, the convergence of the solutions is also checked by a convergent series method known as the homotopy analysis method (HAM). The study examines the influence of several key parameters, including the radius of curvature, Weissenberg number, Prandtl number, Lewis number, Brownian and thermophoretic diffusions parameters, Hartmann number, heat generation parameter, activation energy parameter, temperature difference parameter, chemical reaction parameter, and power law index. The effects of these parameters on momentum, temperature, concentration distributions, mass and heat transfer rates, and as well as the skin friction coefficient are examined through graphs and tables. Graphical observations declare that the velocity field diminishes against the rising values of the Hartmann number and Weissenberg number. However, the velocity profile rises with improved values of the radius of curvature parameter and power law index parameter. It is also noticed that the magnitude of the concentration field rises with growing values of the Brownian parameter, activation energy parameter and Lewis number, whereas it shows a decreasing manner against the enhanced values of the thermophoresis parameter and temperature difference parameter.

Robust and accurate numerical framework for multi-dimensional fractional-order telegraph equations using Jacobi/Jacobi-Romanovski spectral technique

This paper presents a novel spectral algorithm for the numerical solution of multi-dimensional fractional-order telegraph equations, a critical model used to capture the combined effects of diffusion and wave propagation. The core innovation of this work is the application of Jacobi-Romanovski polynomials as the basis functions for spectral discretization. These polynomials offer unique advantages, including the ability to handle nonstandard domains and boundary conditions, making them particularly suitable for partial differential equation (PDE) applications. A comprehensive error analysis is conducted, providing deep insights into the convergence rates and factors affecting the accuracy of the numerical solutions. Extensive numerical experiments further demonstrate the superior performance of the proposed spectral algorithm in solving a wide range of multi-dimensional fractional-order telegraph equation models. The results show a significant improvement in accuracy and computational efficiency compared to traditional numerical methods, such as finite difference or finite element techniques. This research advances the field of computational science by offering a robust, efficient, and versatile numerical framework for the precise solution of complex multi-dimensional PDEs.

Enhancing valuation of variable annuities in Lévy models with stochastic interest rate

This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed minimum benefits in a Lévy equity market environment by incorporating a stochastic interest rate described by the Hull-White model. This approach frames a more dynamic and realistic financial setting compared to previous literature. We exploit a robust valuation mechanism employing a hybrid numerical method that merges tree methods for interest rate modeling with finite difference techniques for the underlying asset price. This method is particularly effective for addressing the complexities of variable annuities, where periodic fees and mortality risks are significant factors. Our findings reveal the influence of stochastic interest rates on the strategic decision-making process concerning the surrender of these financial instruments. Through comprehensive numerical experiments, and by comparing our results with those obtained through the Longstaff-Schwartz Monte Carlo method, we illustrate how our refined model can guide insurers in designing contracts that equitably balance the interests of both parties. This is particularly relevant in discouraging premature surrenders while adapting to the realistic fluctuations of financial markets. Lastly, a comparative statics analysis with varying interest rate parameters underscores the impact of interest rates on the cost of the optimal surrender strategy, emphasizing the importance of accurately modeling stochastic interest rates.

High-Performance Visible-to-SWIR Photodetector Based on the Layered WS2 Heterojunction with Light-Trapping Pyramidal Black Germanium.

This study presents a layered transition metal dichalcogenide/black germanium (b-Ge) heterojunction photodetector that exhibits superior performance across a broad spectrum of wavelengths spanning from visible (vis) to shortwave infrared (SWIR). The photodetector includes a thin layer of b-Ge, which is created by wet etching of germanium (Ge) wafer to form submicrometer pyramidal structures. On top of this b-Ge layer, the WS2 thin film is deposited using pulsed laser deposition. In comparison to conventional germanium, b-Ge absorbs about 25% more light between 850 and 1750 nm wavelengths. The WS2/b-Ge photodetector has a peak photoresponsivity of 0.65 A/W, which is more than twice the photoresponsivity of the WS2/Ge photodetector at 1540 nm. Additionally, it shows better responsivity and response speed compared with other similar state-of-the-art photodetectors. Such an improvement in the performance of the device is credited to the light-trapping effect enabled by the germanium pyramids. Theoretical simulations employing the finite-difference time-domain technique help validate the concept. This novel photodetector holds promise for efficient detection of light across the vis to SWIR spectrum.

Improved numerical schemes to solve general fractional diabetes models

In this article, we propose a new class of nonlinear fractional differential equations of diabetes disease based on the concept of Caputo fractional derivative. Two numerical techniques are introduced to analyse the solution of the general fractional diabetes model, that describes glucose homeostasis. The first method, which constructed using the nonstandard finite difference technique involves an asymptotically stable difference scheme. This method maintains important properties of the solutions of the studied system, such as the positivity and boundedness. The second method is the Jacobi-Gauss–Lobatto spectral collocation approach, known for its exponential accuracy. By employing this collocation method, the problem is transformed into a set of algebraic nonlinear equations, simplifying the overall task. Numerical simulations were conducted to compare the performance of these two techniques with other standard methods and the analytic solution in specific cases. Our findings show that the Jacobi-Gauss–Lobatto spectral collocation technique provides higher accuracy in solving the fractional diabetes model system, while the nonstandard finite difference approach requires lower computational duration.

Dynamics of Fourier's and Fick's laws on the convectively heated oscillatory sheet under Arrhenius kinetics: The finite-difference technique

The significance of chemical reaction with activation energy and convective boundary conditions on the fluid flow via an oscillatory stretchy surface in the presence of permeable media and radiation is analyzed in this study. This inspection presents Fourier and Fick's laws-based equations for heat, mass transport, and liquid flow through an oscillating stretchy sheet. Understanding these dynamics aids in the optimisation of catalytic reaction settings, where gradients greatly influence reaction rates in concentration and temperature. The governing differential equations of the current study are modelled and changed into their non-dimensional form by employing suitable similarity variables. The finite difference method (FDM) is also used to numerically solve the obtained dimensionless equations. The influence of many factors on the several profiles is portrayed with graphical representations. The outcome of the unsteadiness and porosity parameters on the velocity profile with time coordinate is depicted. The increase in the radiation parameter and Biot number upsurges the thermal profile. The temperature reduces as the unsteadiness parameter and temperature relaxation time parameter grow. The upsurge in the activation energy parameter intensifies the mass transport. The rise in concentration relaxation time parameter diminishes the concentration profile.

Finite difference analysis for entropy optimized nanomaterial Darcy-Forchheimer flow with homogeneous and heterogeneous reactions

Hybrid nanoliquids are not underestimated for their involvement in microelectronics, transportation, coolant processes, ships, biological processes and power generation. Hence motivation for current work is to examine homogeneous-heterogeneous reactions in entropy optimized flow by curved sheet stretched with nonlinear velocity. Trihybrid nanoliquid is synthesized through 2 % of ferrous oxides(Fe3O4), 2 % of silver(Ag) and 2 % of copper(Cu). Kerosene oil is employed as the base fluid. These specific kinds of nanoparticles are taken into consideration because of their numerous applications in heat dissipation, air filters, dynamic sealing, biosensors and catalysts process. Kerosene oil may have applications in many different domains such as energy storage, cleaning agent, portable heaters, fuel additive and industrial lubricants. Darcy-Forchheimer model is employed. Analysis in presence of radiation, dissipation, Ohmic heating, entropy generation and heat generation/absorption are organized. Unlike the previous considerations, the thermal expression here consists of impacts through Darcy-Forchheimer relation. Adequate transformations are implemented. Computations have been arranged by applying finite difference technique (FDM) using MATLAB. Quantities for physical interest are addressed. The presented analysis may have relevance for solar systems, chemical reacting processes, cooling towers and polymer data processes. The conclusions are also organized for important key findings. It is noticed that trihybrid nanomaterial has more entropy rate when compared with hybrid and classical nanoliquids when volume fraction is chosen as 2 % for trihybrid fluid. It is proposed that the ability to transfer heat is enhanced when nanoparticles are added to conventional fluids. Decay in concentration is noticed for both homogeneous and heterogeneous parameters. Reduction for Bejan number is noticed through homogeneous diffusion factor. Comparison with previous study is also presented and found great consensus between them.

Investigating new solutions for a general form of q$$ \mathfrak{q} $$‐deformed equation: An analytical and numerical study

SummaryThis paper contributes to the study of a new model called the ‐deformed equation or the ‐deformed tanh‐Gordon model. To understand physical systems with violated symmetries. We utilize the ‐expansion approach to solve the ‐deformed equation for specific parameter values. This method generates solutions that provide valuable insights into the system's dynamics and behavior. To verify the accuracy of our solutions, we also apply the finite difference technique to obtain numerical solutions to the ‐deformed equation. This dual approach ensures the reliability of our results. We present our findings using tables and graphics to enhance clarity and facilitate comparison between the analytical and numerical solutions. These visual aids help readers better understand the similarities and differences between the two approaches. The ‐deformation is significant as it models physical systems with nonstandard symmetry features, like extensivity, offering a more accurate representation of real‐world phenomena. The growing significance of this equation across various disciplines highlights its potential in advancing our understanding of complex physical systems. This paper contributes valuable knowledge about the ‐deformed equation, demonstrating its potential for accurately modeling physical systems with violated symmetries. Through both analytical and numerical techniques, we offer comprehensive solutions and validate their accuracy, with graphical representations enhancing the clarity and understanding of our results. This exploration of ‐deformation advances modeling techniques, providing a more precise depiction of real‐world processes with nonstandard symmetry features.

Numerical Method for Predicting Transient Aerodynamic Heating in Hemispherical Domes

In this research, a streamlined numerical approach designed for the quick estimation of temperature profiles across the finite thickness of a hemispherical dome subjected to aerodynamic heating is introduced. Hemispherical domes, with their advantageous aerodynamic, structural, and optical properties, are frequently utilized in the front sections of objects traveling at supersonic velocities, including missiles or vehicles. The proposed method relies on one-dimensional analyses of fluid dynamics and flow characteristics to approximate the local heat flux across the exterior surface of the dome. By calculating these local heat flux values, it is also possible to predict the temperature variations within the thickness of the dome by employing the finite difference technique, to solve the heat conduction equation in spherical coordinates. This process is iterated over successive time intervals, to simulate the entire flight duration. Unlike traditional Computational Fluid Dynamics (CFD) simulations, the proposed strategy offers the benefits of significantly lower computational time and resource demands. The primary objective of this work is to provide an efficient numerical tool for evaluating aerodynamic heating impact and temperature gradients on hemispherical domes under specific conditions. The effectiveness of the proposed method will be validated by comparing the temperature profiles derived for a standard flight scenario against those obtained from 2-D axisymmetric transient CFD simulations performed using ANSYS-Fluent 2022 R2.

Entropy generation analysis of oscillatory magnetized darcian flow of mixed thermal convection and mass transfer with joule heat over radiative sheet

Significance of this work is to examine enhanced thermal efficiency of magnetic nanofluid in the presence of Joule heating and radiation in missile technological devices, nuclear energy plants, rockets, solar energy systems and enhancing cyclic processes. Prominent aim of current investigation is to demonstrate the amplitude and oscillating analysis of mixed convective heat rate of Darcian magnetic nanoparticle movements with entropy generation, thermal radiation and Joule heat impact through porous stretching sheet. The magnetic layer along stretching surface plays important role to control thermal performance. Governing mathematical equations are reduced in convenient form by using non-dimensional analysis. The primitive mathematical form of steady and oscillating model is calculated through oscillatory stokes and primitive variables. Using Gaussian elimination and finite differences techniques, the geometrical and numerical outcomes of steady and oscillatory models are obtained by applying FORTRAN lahey-95 programming tool. The novelty of this problem is to study the oscillatory thermal and concentration profiles of Darcian magnetic nanoparticles with Joule heating and radiations. It is examined that momentum and temperature distribution grows as radiant-energy increases but decreases for maximum Joule heating. It is found that temperature and concentration distributions enhances as magnetic force decreases. Prominent enhancing amplitudes in heat and mass transfer are obtained for maximum Schmidt and thermophoresis parameter. Heat and mass transfer decreases as magnetic factor increases due to insulating magnetic nanoparticles.

Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification

AbstractThermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.

A Qualitative Analysis of Leukemia Fractional Order SICW Model

Using a series of fundamental differential equations, including the Caputo derivative, which makes it easier to specify the initial conditions of the differential equations, we present a fractional order concept of leukemia in this study. The universality, positivity, and boundedness of solutions are first established. The local stability properties of the equilibrium are studied using the fractional Routh-Hurwitz stability criteria. The differential equation system has been solved using unconventional finite difference techniques. The Leukemia Fractional Order SICW model introduces several innovative elements compared to traditional epidemiological and disease models. This stands out due to its integration of fractional-order differential equations, inclusion of leukemic cells and immune cells compartments, simulation of treatment strategies, consideration of waning immunity, and its application to leukemia-specific scenarios. These elements collectively make it a valuable tool for studying leukemia dynamics, exploring treatment options, and improving our understanding of how the immune system interacts with cancer cells in leukemia patients. Numerical simulations of the model are shown at the conclusion to interpret our theoretical outcomes in support of various fractional orders of derivative options. From there, we can observe how the evolution of the system components is impacted by the fractional derivative .

Facile modification method for the controlled synthesis of dumbbell-like gold nanoparticles (AuNDBs) for application in detecting glucose using the SERS method

Dumbbell-like nanoparticles, previously known for their excellent light absorption and dispersion, have diverse applications, especially in SERS. Herein, we have explored a fast and novel controlled synthesis approach to achieve a high formation of AuNDBs. Precise control of precursor amounts and seed addition order halted seed growth at the AuNDB formation stage, preventing further elongation into rod-like structures. The AuNDBs were functionalized with 4-mercaptobenzoic acid (4-MBA) to create SERS nanosubstrates and deposited on the glass slide through 3-mercaptopropyl (dimethoxy)methylsilane by the spin-coating technique. The detection of d-glucose was achieved by measuring the signal decrease of the 4-MBA Raman probe molecules on the nanosubstrates at different trace concentrations of the analyte. These novel SERS substrates have the potential to provide an enhancement factor (EF) of 2.41 × 107 and a limit of detection (LOD) as low as 1.17 nmol/L. The electromagnetic field distribution of AuNDBs with many arrangements surrounded by air and d-glucose solutions was also determined by using the finite-difference time-domain technique (FDTD). The FDTD results confirmed that d-glucose on the SERS substrates caused the local electromagnetic field to degrade, resulting in the degree of the Raman signal. Our findings suggest that dumbbell-shaped SERS substrates can effectively detect very low levels of glucose, making them ideal for designing novel anisotropic nanoparticle-functionalized surfaces with ease.

Influence of an inclined thick partition on free convection heat transfer performance under surface radiation in a hollow block

In the present work, a computational analysis of the combined energy transfer by free convection, radiation, and heat conduction in 2D hollow block with an inclined partition was carried out. The inclined partition was made of a heat-conducting material and had a finite thickness. The closed space inside the brick was filled with air (Pr = 0.71) and the airflow is laminar. The external surfaces of the vertical borders are considered to be isothermal, and the remaining horizontal surfaces are supposed to be adiabatic. The finite difference technique is employed to work out numerically the differential equations. The in-house computational code was verified in detail using various problems. The major characteristics that determine the considered phenomena are surface emissivity of internal walls, Ra number, and material of solid walls and partition. As a result of the research, the distributions of streamlines and isotherms combined with the average Nusselt numbers were obtained. Depending on the material of the partition, the flow structure in the cavity changes significantly, which reflects the distribution of streamlines, namely, for the materials with low thermal conductivity the convective cell in the upper part of the cavity is elongated, while in the lower part it is shifted to the lower and left borders. The isotherms reflect the more intensive heating in the left part of the area. With an increase in the thermal conductivity coefficient, the streamlines reflecting the nature of the flow are restructured. It was shown that the presence of an inclined partition significantly reduces the intensity of convective heat transfer.

Turbulent and non-turbulent analysis of thermomagnetic convection and heat transfer of darcian radiative nanofluid flow across inclined stretching surface in microgravity environment

Turbulent and non-turbulent analysis of thermomagnetic convection, heating rate and mass transport of Darcian radiating nanofluid flow through porous slanted sheet is the aim of present study. Influence of microgravity is more useful for the movement of thermophoresis nanoparticles with maximum temperature and density. Joule heating, porous medium, magnetic field and thermal radiations are incorporated for the performance of thermal convection. Governing equations are reduced in dimensionless form. Oscillatory stokes conditions are applied to separate the steady, real and imaginary equations. Finite difference, Primitive transformation, and Gaussian elimination techniques are applied for numerical outputs. For asymptotic results, the appropriate range of parameters such as 0.1≤JH≤15.0, 0.1≤Pr≤12.0, 0.1≤Rd≤25.0, 0.0≤λT≤5.0, 0.1≤NT≤1.0, 0.1≤Fr≥6.0, and 0.1≤δ≤1.0 is utilized. Main novelty of work is to examine the steady state and oscillatory behavior of friction-rate, heat/mass transport over slanted two-angles π/6 and π/4. Maximum amplitude in fluid velocity is observed by increasing radiations and buoyant forces. Temperature distribution and nanomaterial concentrations enhance as Joule-heating and Prandtl number increases under microgravity region. Amplitude and oscillation of heat and mass rate is increased as reaction rate, Joule heating and Forchheimer parameter increases. Enhancing behavior of energy transport is observed for maximum choice of Prandtl index with small magnetic effects. It is depicted that high rate of oscillating frequency in heat transmission is detected with maximum radiation effects.

Turbulence generation in the solar corona through nonlinear interaction between 3D kinetic Alfvén wave and magnetic islands

This study investigates the interaction between kinetic Alfvén waves (KAWs) and magnetic islands in solar corona region. KAWs and magnetic islands are believed to be one of the key players in the heating of the coronal plasma and particle acceleration. We have used the dynamical model for KAWs to simulate its propagation through magnetic islands. The equation is solved numerically by using the finite difference and pseudospectral technique for spatial and temporal variations. The simulation results have been studied and signatures of turbulent structures evolving with time have been observed. Turbulence plays a considerable role in tapping out magnetic energy to thermal energy. The plot of the energy spectrum as a function of wavenumber exhibits a power law behavior in the inertial range, characterized with an exponent around −5/3 . Beyond this range, the spectrum becomes steeper. In order to gain a more thorough knowledge of the physical processes that underlie the development of localized structures and to estimate the current sheet scale sizes, a semi-analytically model is also performed. The results indicate that the size of localized structures are comparable to ion gyro-radius, and different intensities of KAW further modify this length scale formed at different times. The purpose of the study is to acquire an understanding of the KAW propagation in magnetic islands and the way it contributes to the formation of turbulence and energy release in the solar corona. A comparative aspect of the non-linear interaction of 3D KAW with magnetic island and null point is also presented which shows that non-linear interaction of 3D KAW with null point, leads to rapid disorganization of the magnetic field and the creation of localized structures.

A comparison of Finite difference schemes to Finite volume scheme for axially symmetric 2D heat equation

In this work, we compare finite difference schemes to finite volume scheme for axially symmetric 2D heat equation with Dirichlet and Neumann boundary conditions. Using cylindrical coordinate geometry, we describe a mathematical model of axially symmetric heat conduction for a stationary, homogeneous isotrophic solid with uniform thermal conductivity in a hollow cylinder with an exact solution in a particular case. We obtain the numerical solution of the PDE adapting finite difference and finite volume discretization techniques. Compared to the exact solution, we explore that the numerical schemes are the sufficient tools for the solution of linear or nonlinear PDE with prescribed boundary conditions. Furthermore, the numerical solution discrepancies in the results obtained from Explicit, Implicit and Crank-Nicolson schemes in Finite Difference Method (FDM) are extremely close to the exact solution in the case of Dirichlet boundary condition. The solution from the Explicit scheme is slightly far from the exactsolution and the solutions from Implicit and Crank-Nicolson schemes are extremely close to the exact solution in the case of Neumann boundary condition. Likewise, the numerical solutions obtained in the Finite volume method (FVM) are extremely close to the exact solution in the case of the Dirichlet boundary condition and slightly away from the exact solution in the case of the Neumann boundary condition.

Line-Based High-Order Hybrid Scheme on Unstructured Grids for Compressible Flows

This study explores the use of line-based finite difference techniques on unstructured grids employing high-order stencils for practical aerodynamic applications. The primary focus is on finite-difference explicit and compact spatial discretization up to sixth order. Problems studied include compressible flows containing discontinuities, which necessitated the use of a hybrid finite difference–finite volume approach, where the former is shown to be effective and accurate for smooth regions, while the latter is robust in capturing discontinuities and shocks. To differentiate between discontinuous and smooth zones, two distinct shock indicators are used, one based on pressure gradients and the other on the divergence of velocity. To achieve faster convergence, spatial discretization is applied with line-based alternating direction implicit (ADI) time integration. A key focus of this work is to demonstrate the proposed methodology in flow scenarios relevant to aircraft applications that also test various aspects of the methodology. Consequently, the cases studied are isentropic vortex convection, standing normal shock, transonic NACA0012 airfoil, supersonic cylinder, unsteady flow past tandem circular cylinders, and supersonic flow past a forward-facing step. Comparisons were also done against an existing line-based finite-volume technique for unstructured grids that employed Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and fifth-order Weighted Essentially NonOscillatory (WENO5) spatial reconstruction schemes. It is observed that the hybrid finite difference–finite volume approach performed well with excellent agreement against available results, sometimes with far fewer degrees of freedom. Furthermore, the implicit ADI scheme is effective over unstructured grids and provides a three-time speed-up over the traditional Runge–Kutta fourth-order scheme.