Cavity Problem Research Articles

Comparison of Post-auricular Soft Tissue and Post-auricular Soft Tissue With Autologous Bone Pate in Obliteration of the Canal Wall Down Mastoidectomy Cavity.

Background The surgical management of chronic otitis media (COM) withsquamous disease is canal wall down mastoidectomy (CWDM). Canal wall down procedures require the obliteration of the newly formed cavity to mitigate complications. Soft tissue flaps, including Rambo flap, Hong Kong flap, Palva flap, and inferior-based fascio-periosteal flap, as well as autologous bone pâté, have been the most successful and commonly used materials for obliteration over the past two decades. Although each flap has its advantages, the Palva flap is considered superior, primarily because of its ease of use and the simplicity of its design. In this study, we intend to evaluate the effectiveness of mastoid obliteration using autologous bone pate with Palvaflap compared to Palvaflap (post-auricular fibro-periosteal soft tissue) in patients who underwent CWDM. Methods Sixty-two patients with COMwith squamous disease were included in the study. The patients underwent CWDM with tympanoplasty and meatoplasty, followed by cavity obliteration using two different methods: group A - obliteration with Palvaflap (post-auricular fibro-periosteal soft tissue) and group B - obliteration with Palvaflap and bone pate. The patients were evaluated for cavity problems on post-operative days 21, 30, 60, 90, and 180, based on a 10-point scale compiled from the literature. Results Our study found that the majority of patients had right-sided disease and were between 41 and 60 years of age. Five out of sixty-two (8.1%) patients developed cavity problems, three in group A (9.7%) and two in group B (6.5%). The incidence of cavity problems was almost the same in both groups. The cavity problems were as follows: vertigo (1/62, 1.6%), surgical site infection (2/62, 3.2%), and graft failure (2/62, 3.2%). However, there were no statistically significant differences (p-value: 0.62) between either of the obliteration methods in terms of mitigating cavity problems. Conclusion Post-auricular soft tissue and post-auricular soft tissue with autologous bone pate in the obliteration of the CWDM cavity provided similar results in terms of mitigating cavity problems.

An Unstructured Mesh Coordinate Transformation‐Based FDTD Method

ABSTRACTWe propose a novel unstructured mesh finite‐difference time‐domain (FDTD) method for solving electromagnetics problems with complicated geometries. The method, which solves the TE‐mode reduced form of Maxwell's equations, can handle both material interfaces and anisotropic material. Using the transformation optics principle, which describes how fields and material tensors change under coordinate transformations, we locally transform each cell in the mesh to a reference unit‐square computational domain where the usual FDTD update is performed. This comes at a cost: employing unstructured grids and coordinate transformations requires more complicated data structures, a mesh orientation process, and potentially introduces an anisotropic material tensor at every mesh cell. Nonetheless, we find that the method maintains the same desirable properties of the classic FDTD method (explicit, divergence‐free B‐field, nondissapative, and second‐order accuracy) while also gaining conforming material interfaces and boundaries in complicated geometry. Even further, we prove that the method is stable under a Courant condition and a fairly nonrestrictive mesh condition, hence defeating the late‐time stability issue plaguing prior nonorthogonal FDTD methods. To verify the method, we conduct convergence studies on three electromagnetic cavity problems with known exact solutions. For these numerical studies, we find that the method maintains second‐order convergence and stability.

A new higher-order super compact finite difference scheme to study three-dimensional non-Newtonian flows

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed higher-order compact finite difference scheme to solve 3D non-Newtonian flow problems. The proposed scheme is fourth-order accurate in space and second-order accurate in time, utilizing only seven adjacent grid points at the (n+1)th time level for the finite difference discretization. A time-marching methodology is employed with pressure calculated via a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning (n = 0.5), shear-thickening (n = 1.5), and Newtonian (n = 1.0) fluids across different Reynolds numbers (Re=1,50,100,200). Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. It is found that for shear-thinning fluid (n = 0.5), u velocity is higher near the top moving wall than the case of Newtonian (n = 1.0) and shear-thickening fluid (n = 1.5) for all Re values. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

Preparation and properties of tellurite glass-based CsPb(BrCl)3@glass fluorescent film for a white light emitting diode color converter

Perovskite nanocrystal glass has the advantages of narrow-band emission, easy tuning, and stable structural, physical, and chemical properties, and can be used to mix with other colored materials for white light modulation. The current white light mode widely adopts the packaging method of blue light chip and yellow phosphor, which has the problem of a blue-yellow cavity and low light quality. In this work, the central wavelength of CsPb(BrCl)3 can be adjusted continuously ranging from 463 nm to 486 nm by adjusting the relative ratio of bromine to chlorine in nanocrystals. On the basis of the previous design of YAG:Ce phosphor-in-glass, perovskite nanocrystal glass powder as a color compensator was introduced into the tellurite glass matrix to form a doubly encapsulated system by low-temperature co-sintering. The yellow phosphor and perovskite nanocrystal glass maintain good structural integrity in the glass matrix. By combining the double-package fluorescent material with the blue chip, the continuous adjustment of chromaticity coordinates along the saddle line is realized, and the color-rendering index is also improved to 81.3.

Causes and Hazards of Perimeter Rock Cavities behind Shield Tunnels

The purpose of this paper is to discuss the reasons for the generation of voids in the surrounding rock behind water transmission shield tunnels and the potential hazards they bring. Firstly, it analyzes in detail the possible causes of cavities from the aspects of geological conditions, construction technology, material properties, etc. On the basis of literature research, the causes and distribution patterns of the perimeter rock cavities behind the water transfer shield tunnels were explored with respect to the locations and sizes of the cavities behind the tube sheets. Secondly, it systematically elaborates the hazards of cavities on tunnels from the aspects of structural stability, use function, operation safety, etc. Finally, it proposes corresponding preventive measures and countermeasures for the problem of cavities. This paper aims to provide valuable reference for the design, construction and operation management of shield tunnels, which is of great theoretical significance and practical value for the safe construction and long-term operation of shield tunnels.

Indications and outcomes of subtotal petrosectomy: our experience and review of literature

BackgroundSubtotal petrosectomy (STP) has attracted massive interest over last two decades. The aim is to present our experience of this uncommon surgery. The indications, outcomes, and our variation in surgical technique would be presented and literature reviewed.MethodsA retrospective observational study of all patients who underwent STP at a tertiary care center in India was analyzed.ResultsA total of 9 ears (in 8 patients) underwent STP over last 5 years at our center. The pathological conditions for which STP was done included chronic otitis media squamous (four ears), middle ear tumors (three ears), petrous apicitis (one ear), and traumatic cerebrospinal fluid (CSF) otorhinorrhea (one ear). The indication of STP included disease clearance (eight ears), unserviceable hearing (seven ears), hearing rehabilitation with otological implants (six ears), and intraoperative CSF gusher (one ear). Intraoperative indications included CSF gusher, large tegmen defect with erosion of apical turn of cochlea, and erosion of anterior bony wall of external auditory canal. The mean follow-up period was 36 months (range of 6 months to 60 months). None of the patients had any dehiscence of blind sac closure or secondary acquired cholesteatoma on imaging.ConclusionsSTP facilitates disease clearance by providing unmatchable exposure in difficult otological scenarios and additionally isolates middle ear cleft from external environment, thereby eliminating problems of mastoid cavity. Furthermore, it also prepares ear for second stage otological implants. It is a safe surgery with minimal complications.

Variant slip effects, aspect ratios and steady-state criteria in unsteady cavities with direct PDE simulation of eddies

Abstract Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate the formation of eddies under different aspect ratios and steady-state criteria. A couple of nonlinear unsteady partial differential equations (PDEs) of Navier Stokes satisfying a set of boundary conditions is examined with both inclusions of no-slip and free-slip effects. Finite difference method (FDM) is employed to solve the vorticity-stream function using a self-developed Matlab® code embedded in a Graphical User Interface (GUI) to ease the cavity problem analysis by the end users. Four models are studied where Ansys Fluent® employing the Finite Element Method (FEM) is used to verify the present FDM steady-state results produced for the first model. It is observed that the value of stream function begins to drop and streamline distribution changes shape when e ≤ 10−5. Refrainment of merging of secondary eddies also happens when the free-slip boundary condition effect passes the threshold value. The Stretching effect with free-slip BC in the fourth model regulates the fluid dynamics to reach the entire cavity sufficiently with no room for eddy formation by increasing the slip length to an intense value. Free-slip simulates free surface applications in geophysical occurrences (river and glacier), spilling dynamics, ship hull designs, technologies of coating and fuel spraying/injection.

On the resonance frequency of the irregular shaped visco-acoustic Helmholtz cavity problem

In this paper we develop a closed-form mathematical solution for the resonance frequency of the axisymmetric irregular shaped visco-acoustic Helmholtz cavity problem. The solution is based on a conformal mapping that transforms the governing visco-acoustic equations of motion for the irregular cavity geometry into a new domain described by a set of orthogonal curvilinear coordinates. These orthogonal curvilinear coordinates have an important characteristic relative to the transformation of the physical boundary: the mapped domain is constructed such that the locus of all points for the length-wise profile of the physical boundary coincides with a constant value for a (quasi radial) coordinate in the new mapped domain. In these orthogonal curvilinear coordinates we obtain an analytical solution for the visco-acoustic equations of motion and exactly satisfy the no-slip fluid boundary conditions over the irregular shaped cavity walls by matching the coefficients of an orthogonal Legendre polynomial series representation for the non-uniform velocity on the cavity walls. The mathematical solution is an approximation to the extent that the scale factors chosen for the mapping consist of strictly the mutual-coupling terms of the true scale factors. Thus we analyze some results to understand the correlation of the analytical solution frequency response spectra with numerical finite element analyses of the idealized boundary conditions with various irregular shaped cavity geometries. The results for fundamental resonance frequency were found to exhibit good correlation with the results of finite element analyses over a significant range of fluid properties with different irregular cavity geometries. As the primary motivation for the derivation stems from the lack of a rapid yet accurate alternative to computationally intensive MultiPhysics FEA in the formulation of acoustic trendlines for sensor development, the solution’s acoustic impedance was applied as dispersive loading in a simple lumped parameter model of a fluid identification sensor for comparison. The resulting acoustic trendlines of the reduced (5 DOF) model were found to exhibit good correlation with the results of the MultiPhysics FEA (>105 DOF). Thus the solution was found to enable a closed-form analytical method for rapid construction of parametric studies in the practical design of fluid analysis sensors based on complex resonant cavity geometries.

Resorbable engineered barrier membranes for oral surgery applications.

Population aging, reduced economic capacity, and neglecting the treatments for oral pathologies, are the main causal factors for about 3 billion individuals who are suffering from partial/total edentulism or alveolar bone resorption: thus, the demand for dental implants is increasingly growing. To achieve a good prognosis for implant-supported restorations, adequate peri-implant bone volume is mandatory. The Guided Bone Regeneration (GBR) technique is one of the most applied methods for alveolar bone reconstruction and treatment of peri-implant bone deficiencies. This technique involves the use of different types of membranes in association with some bone substitutes (autologous, homologous, or heterologous). However, time for bone regeneration is often too long and the bone quality is not simply predictable. This study aims at engineering and evaluating the efficacy of modified barrier membranes, enhancing their bioactivity for improved alveolar bone tissue regeneration. We investigated membranes functionalized with chitosan (CS) and chitosan combined with the peptide GBMP1α (CS + GBMP1α), to improve bone growth. OsseoGuard® membranes, derived from bovine Achilles tendon type I collagen crosslinked with formaldehyde, were modified using CS and CS + GBMP1α. The functionalization, carried out with 1-ethyl-3-(3 dimethylaminopropyl)carbodiimide and sulfo-N-Hydroxysuccinimide (EDC/sulfo-NHS), was assessed through FT-IR and XPS analyses. Biological assays were performed by directly seeding human osteoblasts onto the materials to assess cell proliferation, mineralization, gene expression of Secreted Phosphoprotein 1 (SPP1) and Runt-Related Transcription Factor 2 (Runx2), and antibacterial properties. Both CS and CS + GBMP1α functionalizations significantly enhanced human osteoblast proliferation, mineralization, gene expression, and antibacterial activity compared to commercial membranes. The CS + GBMP1α functionalization exhibited superior outcomes in all biological assays. Mechanical tests showed no significant alterations of membrane biomechanical properties post-functionalization. The engineered membranes, especially those functionalized with CS + GBMP1α, are suitable for GBR applications thanks to their ability to enhance osteoblast activity and promote bone tissue regeneration. These findings suggest a potential advancement in the treatment of oral cavity problems requiring bone regeneration.

A new compact scheme-based Lax–Wendroff method for high fidelity simulations

The classical Lax–Wendroff (LW) method employs explicit second order central difference schemes to solve partial differential equations. Recently, the authors in Sengupta et al. (2023) have identified numerical parameter ranges in performing large eddy simulation (LES) using this classical LW method. In a bid to improve these numerical parameter ranges for high fidelity computations, a new non-uniform grid based compact scheme for LW method (NUCLW) is developed here. This new method uses sixth order non-uniform compact scheme (NUC6) for the first and higher order derivatives. Reported global spectral analysis confirms substantial improvement in the resolution and accuracy of NUCLW scheme over the classical LW scheme. A significant advantage of the present scheme is its ability to compute solutions for non-uniform, structured grids, and that does not suffer degradation in accuracy. The potential of the NUCLW scheme for high accuracy computations is demonstrated by solving 2D incompressible Navier–Stokes equations for the benchmark unsteady flow inside a square lid driven cavity problem for a subcritical Reynolds number of 3200 and a post-critical Reynolds number of 10,000 and simulating the instability of the Taylor–Green vortex problem. These demonstrate the ability of the NUCLW scheme to solve the Navier–Stokes equations for high fidelity simulations such as LES/DNS with enhanced ranges of numerical parameters with respect to enhanced accuracy and faster computations.

Comparative analysis of nondimensionalization approaches for solving the 2‐D differentially heated cavity problem

AbstractThis work reports a numerical study on the effect of three nondimensionalization approaches that are commonly used to solve the classic problem of the 2‐D differentially heated cavity. The governing equations were discretized using orthogonal collocation with Legendre polynomials, and the resulting algebraic system was solved via Newton–Raphson method with LU factorization. The simulations were performed for Rayleigh numbers between 103 and 108, considering the Prandtl number equal to 0.71 and a geometric aspect ratio equal to 1, analyzing the convergence and the computation time on the flow lines, isotherms and the Nusselt number. The mesh size that provides independent results was 51 × 51. Approach II was the most suitable for the nondimensionalization of the differentially heated cavity problem.

External auditory canal reconstruction using a novel mastoidoplasty technique during canal wall down mastoidectomy: how I do it.

While mastoid obliteration techniques have received much attention in decreasing the disadvantages associated with the resultant mastoid cavity from canal wall down procedures, techniques for an anatomically normal looking ear canal reconstruction to increase the feasibility of hearing aid fitting are less commonly discussed as an alternative. Our mastoidoplasty technique basically utilises an inferiorly based periosteal flap with or without temporalis muscles and fascia to obliterate the epitympanum and reconstruct the external auditory canal (EAC). Stay sutures are used to keep them in place. For larger cavities, demineralized bone matrix (DBM) is used to obliterate the mastoid cavity and support the neo-EAC. The concept of our mastoidoplasty potentially provides a very useful alternative in recreating a near normal ear canal anatomy avoiding cavity problems as well as facilitating hearing aid fitting with canal type hearing aids after canal wall down mastoidectomy.

Mixed Convection in a Lid-Driven Cavity Filled with Nanofluids Using Single- and Two-Phase Eulerian Modeling Methods

The numerical simulation of the classical lid-driven cavity problem has been carried out to investigate the suitability of two-phase flow modeling techniques for nanofluids in computational fluid dynamics. The nanofluid investigated comprises water as base fluid and Al2O3 nanoparticles. Three types of the Eulerian-multiphase models, including the Eulerian, mixture, and volume of fluid (VOF) were compared with the single-phase model. The model equations were solved using ANSYS Fluent software for the nanoparticle volume fraction, the Richardson and Reynolds numbers in the range 0 ≤ ø ≤ 0.10, 10−4 ≤ Ri ≤ 102, and 1 ≤ Re ≤ 1000, respectively at a fixed Grashof number, Gr = 100. The results were compared with that of single-phase nanofluid modeling. There were similarities in the flow structure and temperature distribution for the single-phase and multi-phase methods when the convection is natural and mixed. However, the Nusselt number computed by the mixture and Eulerian models is higher than that of the single-phase and VOF models under the forced convection regime, with the percentage deviation from that of the single-phase as high as 10%. So, the three multiphase models are suitable for nanofluid convection problems and give results comparable to the single-phase model, especially under the natural and mixed convection regimes.

Computational modelling of compressible nonisothermal viscoelastic fluids

The prediction of compressible nonisothermal flows of viscoelastic fluids is important in many industrial processes. Until relatively recently, there was a lack of tractable thermodynamically consistent mathematical models for this class of flows. In this paper a stabilised finite element scheme is presented for the models developed by the authors Mackay and Phillips (2019) which incorporates compressibility and nonisothermal effects. Numerical results are presented for variants of a couple of benchmark problems: the lid driven cavity and the natural convection problems. The temporal discretisation is based on the Taylor–Galerkin method. A compressible version of the discrete elastic viscous split stress (DEVSS) formulation is used to stabilise the numerical scheme. The combined and separate influence of compressible, viscoelastic and thermal effects on the characteristics of these benchmark flows is studied for the first time.

A φ-divergence based finite element moment method for the polyatomic ES-BGK Boltzmann equation

Bonafide numerical simulations of transport phenomena in rarefied gases are becoming increasingly important in science and engineering. To enhance the accuracy of the rarefied-gas model, it is important to account for the internal structure of the gas molecules and exceed the standard monatomic description. A suitable model for polyatomic rarefied-gas flows that balances between accuracy and complexity is the polyatomic ES-BGK Boltzmann equation. In this work we consider numerical approximation of the ES-BGK Boltzmann equation based on a Method of Moments (MoM) approximation in the velocity/internal-energy dependence, and DGFEM approximation in the spatial dependence. In the MoM setting, only two moments have to be considered in internal-energy dependence to capture the correct macroscopic gas properties, viz. the thermal conductivity, the adiabatic coefficient and the shear and dilational viscosity. In the presentation of the method, we focus specifically on the evaluation of the integrals in the velocity and intrinsic-variable dependence appearing in the MoM formulation and on linearization of the formulation. We present numerical results for the heat flux between two parallel heated plates, mass flow in a micro-channel, a poly-atomic lid-driven cavity problem, and rarefied-gas flow around a sphere. The computed results are compared with corresponding theoretical and experimental results. The results support the suitability of the FEM-MoM approximation of the ES-BGK Boltzmann equations as a model for predicting transport phenomena in rarefied-gas flows.

Analysis of steady-state nonlinear problems via gradual introduction of nonlinearity

In this paper, we develop a method that allows one to consider the nonlinearity for all the nonlinear stationary partial differential equations in a gradual way, i.e., via small increments, which inspired us to define it as an incremental approach. The method considers the tensors of the equations as being constituted of two parts, one independent and the other dependent on the solution. The second part is progressively taken into account through a convenient set of parameters. Moreover, we present a scheme that allows the incremental parameters to be always improved, either to ensure that a given iteration solution is within the convergence radius or to reduce the computational cost. Numerical results are presented for various nonlinear stationary partial differential equations, including Navier–Stokes. The results demonstrate the excellent performance of the proposed method, particularly on the lid-driven cavity problem simulated with number of Reynolds equal to 50000. Finally, in the Appendix, we suggest some sets of incremental parameters for some stationary nonlinear problems.

Numerical investigation of store separation from cavity problems at high speeds

In this work, the ability of open-source CFD tools to conduct store separation simulations from cavities is evaluated and validated using a generic test case from the literature. Firstly, the ability and accuracy of these tools for solving cavity flows at high speeds are evaluated. Secondly, their competence in predicting the trajectory of a generic store from a generic deep cavity is checked. Finally, and in order to reduce the associated computational costs, a release-time dependability factor from the recent literature is studied and evaluated. The obtained results using the selected open-source CFD tools matched quite well with the wind tunnel results. Furthermore, the results show that predicting the release-time dependability using a quantified index/factor can be a potential remedy for reducing the computational cost for this type of CFD simulations.

A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite element scheme for the numerical solution of the incompressible viscous and resistive magnetohydrodynamics (MHD) equations on staggered unstructured mixed-element meshes in two and three space dimensions. The equations are split into several subsystems, each of which is then discretized with a particular scheme that allows to preserve some fundamental structural features of the underlying governing PDE system also at the discrete level. The pressure is defined on the vertices of the primary mesh, while the velocity field and the normal components of the magnetic field are defined on an edge-based/face-based dual mesh in two and three space dimensions, respectively. This allows to account for the divergence-free conditions of the velocity field and of the magnetic field in a rather natural manner. The non-linear convective and the viscous terms in the momentum equation are solved at the aid of an explicit finite volume scheme, while the magnetic field is evolved in an exactly divergence-free manner via an explicit finite volume method based on a discrete form of the Stokes law in the edges/faces of each primary element. The latter method is stabilized by the proper choice of the numerical resistivity in the computation of the electric field in the vertices/edges of the 2D/3D elements. To achieve higher order of accuracy, a piecewise linear polynomial is reconstructed for the magnetic field, which is guaranteed to be exactly divergence-free via a constrained L2 projection. Finally, the pressure subsystem is solved implicitly at the aid of a classical continuous finite element method in the vertices of the primary mesh and making use of the staggered arrangement of the velocity, which is typical for incompressible Navier-Stokes solvers. In order to maintain non-trivial stationary equilibrium solutions of the governing PDE system exactly, which are assumed to be known a priori, each step of the new algorithm takes the known equilibrium solution explicitly into account so that the method becomes exactly well-balanced. We show numerous test cases in two and three space dimensions in order to validate our new method carefully against known exact and numerical reference solutions. In particular, this paper includes a very thorough study of the lid-driven MHD cavity problem in the presence of different magnetic fields and the obtained numerical solutions are provided as free supplementary electronic material to allow other research groups to reproduce our results and to compare with our data. We finally present long-time simulations of Soloviev equilibrium solutions in several simplified 3D tokamak configurations, showing that the new well-balanced scheme introduced in this paper is able to maintain stationary equilibria exactly over very long integration times even on very coarse unstructured meshes that, in general, do not need to be aligned with the magnetic field.

Extraction of Lagrangian Coherent Structures in the framework of the Lagrangian–Eulerian Stabilized Collocation Method (LESCM)

In recent years, the investigations on Lagrangian Coherent Structures (LCS) in complex flows have attracted increasing attention due to their ability to accurately describe flow field details. In this study, we propose a novel and accurate numerical technique based on the Lagrangian–Eulerian Stabilized Collocation Method (LESCM) for computing the Finite Time Lyapunov Exponents (FTLEs), which is essential for extracting LCSs in viscous incompressible flows. LESCM, previously employed for simulating fluid–structure interaction problems, was developed based on the Material Point Method (MPM). The hybrid Lagrangian–Eulerian​ description in LESCM enables explicit tracking of fluid flow trajectories throughout the simulation and direct evaluation of the FTLE field. Furthermore. The errors in FTLEs caused by the Particle Shifting Technique (PST) are completely avoided due to the Eulerian characteristic of LESCM as the deformation gradient is calculated based on fixed Eulerian nodes rather than fluid particles with unphysical shifting. Consequently, the novel technique based on LESCM surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex LCSs in flow fields. Additionally, By harnessing the remarkable efficiency of LESCM, MATLAB can now handle up to 16 million particles with ease, eliminating the need for parallel computation techniques. Several numerical examples, such as 2D Taylor-Green​ vortices, flow passing a circular cylinder and a 3-dimensional shear driven cavity problem, have been tested to demonstrate the effectiveness of this novel approach under various conditions.

Computational Study of the Flow of Newtonian Fluid Through A Straight Channel and Lid-Driven Cavity

This article aims to introducenumerical study of two different incompressible Newtonian fluid flows. The first type of flow is through the straight channel, while the second flow is enclosed within a square cavity and the fluid is moved by the upper plate at a specific velocity. Numerically, a Taylor-Galerkin\ pressure-correction finite element method (TGPCFEM) is chosen to address the relevant governing equations. The Naiver-Stoke partial differential equations are usually used to describe the activity of fluids. These equations consist of the continuity equation (conservation of mass) and the time-dependent conservation of momentum, which are preserved in Cartesian coordinates. In this study, the effect of Reynolds number (Re) variation is presented for both problems. Here, the influence of Re on the convergence rate and solution behavior is provided. Findings display that, there is a significant impact of Re upon the temporal convergence rates of velocity and pressure. As well, the rate of convergence increases as the values of Re are risen. For the cavity problem, one can infer that, as the Reynolds number rises, the size of the vortex is reduced.