Journal of Engineering Mathematics最新文献

In this paper, the identification of immersed obstacles in a steady incompressible Navier–Stokes viscous fluid flow from fluid traction measurements is investigated. The solution of the direct problem is computed using the finite element method (FEM) implemented in the Freefem++ commercial software package. The solution of the inverse geometric obstacle problem (parameterized by a small set of unknown constants) is accomplished iteratively by minimizing the nonlinear least-squares functional using an adaptive moment estimation algorithm. The numerical results for the identification of an obstacle in a viscous fluid flowing in a channel with open ends, show that when the fluid traction is measured on the top, bottom and inlet boundaries, then the algorithm provides accurate and robust reconstructions of an obstacle parameterized by a small number of parameters in a Fourier trigonometric finite expansion. Stable reconstructions with respect to noise in the measured fluid traction data are also achieved, although for complicated shapes parameterized by larger degrees of freedom Tikhonov regularization of the least-squares functional may need to be employed. Multiple-component obstacles may also be identified provided that a good initial guess is provided. In case of limited data being available only at the inlet boundary the pressure gradient provides more information for inversion than the fluid traction.

Abstract

Studies on the wetting effect reveal that slip is prevalent at the fluid–solid interface, and its influence cannot be disregarded in microscopic systems. The traditional understanding of the propagation rules and characteristics of elastic waves in fluid-saturated porous media are challenged by the introduction of slip boundary effect. In this paper, the influence of slip boundary effect on the dispersion and attenuation of both shear horizontal guided waves and Love waves in a fluid-saturated porous media is investigated. The virtually enlarged pore model is employed to characterize the degree of slip and the wetting effect with the slip length. It is found that both velocity and attenuation of shear horizontal guided waves in monolayer are sensitive to slip boundary effect, while only attenuation shows sensitivity for Love wave with no significant impact observed on its velocity. The research results fill a gap in understanding how slip boundary effect affects the propagation of shear horizontal and Love waves in fluid-saturated porous media, which is of great significance for the identification of sediment type, physical property inversion and reservoir evaluation.

This paper provides numerical validation of some new explicit, asymptotically exact, analytical formulas describing channel flows over liquid-infused surfaces, an important class of surfaces of current interest in surface engineering. The new asymptotic formulas, reproduced here, were derived in a recent companion paper by the authors. The numerical validation is done by presenting a novel computational method for calculating longitudinal flow in a periodic channel involving finite-length closed liquid-filled grooves with a flat two-fluid interface, a challenging problem given the two-fluid nature of the flow. The formulas are asymptotically exact for wide channels where the grooves on the lower wall of the channel are well separated; the numerical method devised here, however, is subject to no such restrictions. Significantly, it is shown here that the asymptotic formulas remain good global approximants for the flow over a wide range of flow geometries, including those well outside the asymptotic parameter range for which they were derived. It is found that the formulas are more reliable for liquid-infused surfaces than for superhydrophobic surfaces.

The existing six light screen array measuring methodology of uniform linear trajectory is unable to determine the impact coordinate and flight speed of the terminal parabolic trajectory projectile. With the parabola trajectory in the terminal trajectory test as the objective, a method is presented to test the flight characteristics of a projectile with a variable speed parabola trajectory. By accounting for the effects of air resistance and gravity on the projectile's trajectory, the space motion equation for the projectile is determined. The impact position and flight speed of the terminal parabolic trajectory projectile cannot be determined by the current six light screen array measurement approach of uniform linear trajectory. A technique is described to evaluate the flight properties of a projectile with a variable speed parabola trajectory, with the goal being the parabola trajectory in the terminal trajectory test. The space motion equation for the projectile is calculated by taking into consideration the effects of gravity and air resistance on its trajectory. The precision of the measurement algorithm is assessed. The results show that the measurement error of the impact coordinates in the detection target plane is not larger than 3.5 mm. The developed measurement model expands the use of the six light curtain rays in the field of terminal trajectory measurement.

The propagation of shear waves inside/at the Earth’s crust during earthquake may cause the progression of punch in the rock medium. In this study, the movement of semi-infinite punch due to the propagation of the shear wave in a pre-stressed vertically transversely isotropic poro-viscoelastic medium has been analyzed. Based on Wiener–Hopf technique and two-sided Fourier integral transformations, the dynamic stress concentration due to moving punch is determined in closed form. The significant effects of various affecting parameters viz. velocity of moving punch, horizontal initial stress, vertical initial stress, anisotropy parameter, porosity, and viscoelasticity on dynamic stress concentration have been discussed. It is noteworthy that as the punch propagates with higher velocity, dynamic stress concentration in the considered poro-viscoelastic medium escalates. It is also found that horizontal tensile and vertical compressive initial stresses have an adverse impact on the dynamic stress concentration. On the other hand, the horizontal compressive and vertical tensile initial stresses have a favorable influence on the dynamic stress concentration. Also, its values increase with the increase of porosity, while it gets decreased as anisotropic parameter prevails in the considered medium. The behavior of dynamic stress concentration in three different types of pre-stressed vertically transversely isotropic poro-viscoelastic media viz. sandstone (a sedimentary rock), granite (an igneous rock), and marble (a metamorphic rock) has been compared. From this comparison, it is obtained that the dynamic stress concentration attains maximum value if the rock medium is marble and minimum value if the rock medium is sandstonel. Some graphical illustrations and numerical computations have also been established. Furthermore, some important properties are identified from the obtained dynamic stress concentration expressions.

The present work is focussed on analyzing the stability of fluid within the porous structure, accounting for constant internal heat generation by employing both linear (normal mode technique) and nonlinear stability (energy) techniques. The impact of diverse sets of boundary constraints, encompassing impermeable, conducting, porous, and insulating on the stability is also explored. The governing equations are transformed into an eigenvalue problem derived from stability analysis, which is transformed into a fourth-order problem on separating Fourier component and then numerically solved using the Chebyshev pseudospectral method for finding the critical Rayleigh numbers. It is found that the presence internal heat generation gives rise to the potential of subcritical instability. Five models are considered based on bounding surfaces and the impact of internal heating is analysed which suggest that the stability can be enhanced or convection can be accelerated by taking appropriate combination of these models and values of heat generation parameter. It is also noted that in the absence of internal heating the subcritical region of instability does not exist.

This paper addresses the design and validation of High-Order Absorbing Boundary Conditions (HABC) of the Padé family on a Coupled Hydrodynamic Wave Model (CHWM) especially with surface tension effect (with small spatial scales). Inspired by the Neumann–Kelvin model, the CHWM comprises a fluid model enabling the consideration of multiple objects located immediately beneath the surface, coupled with a free surface model that incorporates a small added mass surface term. With the surface tension effect, we introduce new coefficients (similar to Higdon coefficients) on each HABC (for the surface model and the basin model) to ensure the continuity of the two HABC at the interface between the coupled models. Consequently, we propose a useful specific compatibility condition, and a significant reduction of the Padé approximation particularly in the water case.

This paper comprehensively studies effective numerical methods for solving the simplest chaotic circuit model. We introduce a novel scheme for the Atangana–Baleanu Caputo fractional derivative (ABC-FD), coupled with the Laplace decomposition method (LDM). Furthermore, we rigorously compare the performance of these proposed methods with the Runge–Kutta fourth-order method. Using two mathematical techniques, we have discovered effective and highly convergent solutions to the chaotic model. We gave different values to the parameters to plot the chaos and create a phase portrait of the system. Therefore, the provided methods can be applied to more sophisticated examinations of different models. This study advances numerical techniques for understanding chaotic dynamics in complex systems. By introducing a novel scheme for the Atangana–Baleanu Caputo fractional derivative and the Laplace decomposition method, we provide a robust framework for effectively solving the simplest chaotic circuit model. This framework enhances accuracy and efficiency in unraveling chaotic behaviors, contributing to a broader understanding of chaotic dynamics across scientific domains in the future.

This analysis aims to determine the two-phase analysis of thermal transmission on MHD Eyring–Powell dusty hybrid nanofluid flow over a stretching cylinder with non-Fourier heat flux model and the influence of a uniform heat source and thermal radiation. The hybrid nanofluid was formulated by the mixture of Silicone oil-based Iron Oxide ((text{Fe}_{3}text{O}_{4})) and Silver (Ag) nanoparticles flow properties after the mechanism has been filled with dusty particles. The increasing demand for sustainable sources of heat and electricity has inspired significant interest towards the conversion of solar radiation into thermal energy. Due to their enhanced ability to promote heat transmission, nanofluids can significantly contribute to enhancing the efficiency of solar-thermal systems. The non-linear equations for the velocity, energy, skin friction coefficient, and Nusselt number are solved using Bvp4c with MATLAB solver. Tables and graphs are used to show how essential parameters affect fluid transport properties. The temperature profile is decreased with greater Eyring–Powell fluid parameter values. The curvature parameter is intensified for the higher values of the velocity profile. The temperature is influenced by increasing values in the thermal radiation, while it is reduced by rising values in the thermal relaxation parameter. Increasing the value of the curvature parameter leads to a reduction in the skin friction factor. It is revealed that improving the values of the fluid–particle interaction for temperature and curvature parameter decrements for the Nusselt number.