The quarterly journal of mechanics and applied mathematics最新文献_第4页

Coupling Stokes Flow with Inhomogeneous Poroelasticity 非均匀孔隙弹性耦合Stokes流

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-01-01 DOI: 10.1093/qjmam/hbab014

Matteo Taffetani;Ricardo Ruiz-Baier;Sarah Waters

引用次数: 1

Hypersingular Integral Equation Formulation of the Problem of Water Wave Scattering by A Circular Arc Shaped Impermeable Barrier Submerged in Water of Finite Depth 有限深度水中圆弧型不透水屏障对水波散射问题的超奇异积分方程

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-01-01 DOI: 10.1093/qjmam/hbab012

Dibakar Mondal;Anushree Samanta;Sudeshna Banerjea

引用次数: 0

Dam-break reflection 支流蓄反射

The quarterly journal of mechanics and applied mathematics Pub Date : 2021-01-01 DOI: 10.1093/qjmam/hbab010

Andrew J Hogg;Edward W G Skevington

引用次数: 0

Use of a Modal Model in Predicting Propagation from a Point Source Over Grooved Ground 利用模态模型预测槽地面上的点源传播

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-11-01 DOI: 10.1093/QJMAM/HBAA018

Steve Mellish, S. Taherzadeh, K. Attenborough

引用次数: 2

On the Connection Between Step Approximations and Depth-Averaged Models for Wave Scattering by Variable Bathymetry 变水深波散射阶跃近似与深度平均模型的关系

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbaa002

R Porter

{"title":"On the Connection Between Step Approximations and Depth-Averaged Models for Wave Scattering by Variable Bathymetry","authors":"R Porter","doi":"10.1093/qjmam/hbaa002","DOIUrl":"https://doi.org/10.1093/qjmam/hbaa002","url":null,"abstract":"Two popular and computationally inexpensive class of methods for approximating the propagation of surface waves over two-dimensional variable bathymetry are ‘step approximations’ and ‘depth-averaged models’. In the former, the bathymetry is discretised into short sections of constant depth connected by vertical steps. Scattering across the bathymetry is calculated from the product of \u0000<tex>$2 times 2$</tex>\u0000 transfer matrices whose entries encode scattering properties at each vertical step taken in isolation from all others. In the latter, a separable depth dependence is assumed in the underlying velocity field and a vertical averaging process is implemented leading to a second-order ordinary differential equation (ODE). In this article, the step approximation is revisited and shown to be equivalent to an ODE describing a depth-averaged model in the limit of zero-step length. The ODE depends on how the solution to the canonical vertical step problem is approximated. If a shallow water approximation is used, then the well-known linear shallow water equation results. If a plane-wave variational approximation is used, then a new variant of the mild-slope equations is recovered.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"73 1","pages":"84-100"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49963674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation Falkner-Skan边界层方程的渐近逼近

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbz021

E R Belden;Z A Dickman;S J Weinstein;A D Archibee;E Burroughs;N S Barlow

{"title":"Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation","authors":"E R Belden;Z A Dickman;S J Weinstein;A D Archibee;E Burroughs;N S Barlow","doi":"10.1093/qjmam/hbz021","DOIUrl":"https://doi.org/10.1093/qjmam/hbz021","url":null,"abstract":"We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle \u0000<tex>$betapi/2$</tex>\u0000 to the horizontal. A wide range of wedge angles satisfying \u0000<tex>$betain[-0.198837735, 1]$</tex>\u0000 are considered, and the previously established non-unique solutions for \u0000<tex>$beta<0$</tex>\u0000 having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the power series solution to the Falkner–Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Padé approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner–Skan solution at large distances from the wedge.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"73 1","pages":"36-50"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbz021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49963673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 10

Converging shock waves in a Van der Waals gas of variable density 变密度范德华气体中的会聚激波

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbaa003

Antim Chauhan;Rajan Arora;Amit Tomar

{"title":"Converging shock waves in a Van der Waals gas of variable density","authors":"Antim Chauhan;Rajan Arora;Amit Tomar","doi":"10.1093/qjmam/hbaa003","DOIUrl":"10.1093/qjmam/hbaa003","url":null,"abstract":"SUMMARY The converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a non-ideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to the implosion problem and obtained a global solution that also admits Guderley’s asymptotic solution in a very good agreement which holds only in the vicinity of the axis/centre of implosion. The similarity exponents together with their corresponding amplitudes are determined by expanding the flow parameters in powers of time. We also refined the leading similarity exponents near the axis/centre of convergence. We compared our calculated results with the already existing results and found them in good agreements up to two decimal places. Shock position and flow parameters are analysed graphically with respect to the variation of values of different parameters. It is observed that an increase in the density variation index, adiabatic exponent and Van der Waals excluded volume, causes the time of shock collapse to decrease due to which the shock acceleration gets increased and shock reaches the axis/centre much faster.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"73 1","pages":"101-118"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48872698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

A Note on Viscous Flow Induced by Half-Line Sources Bounded by Conical Surfaces 关于以圆锥面为界的半线源引起的粘性流动的一个注记

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbz020

Prabakaran Rajamanickam;Adam D Weiss

引用次数: 0

Some Universal Solutions for a Class of Incompressible Elastic Body that is Not Green Elastic: The Case of Large Elastic Deformations 一类非绿弹性不可压缩弹性体的通解:大弹性变形的情况

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbaa006

R Bustamante

引用次数: 4

Image Conditions for Elliptical-Coordinate Separation-of-Variables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers 具有完美反射平边界的椭圆坐标变量分离声学多重散射模型的成像条件:在原位可调噪声屏障中的应用

The quarterly journal of mechanics and applied mathematics Pub Date : 2020-02-01 DOI: 10.1093/qjmam/hbaa005

Ho-Chul Shin

{"title":"Image Conditions for Elliptical-Coordinate Separation-of-Variables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers","authors":"Ho-Chul Shin","doi":"10.1093/qjmam/hbaa005","DOIUrl":"10.1093/qjmam/hbaa005","url":null,"abstract":"SUMMARY Two-dimensional time-harmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedge-shaped acoustic domains including half-plane and right-angled corners. The method of separation of variables in conjunction with the addition theorems is employed in the elliptical coordinates. The wavefunctions are represented in terms of radial and angular Mathieu functions. The method of images is applied to consider the effect of the infinitely long flat boundaries which are perfectly reflecting: either rigid or pressure release. The wedge angle is \u0000<tex>$pi/n$</tex>\u0000 rad with integer \u0000<tex>$n$</tex>\u0000; image ellipses must be appropriately rotated to realise the mirror reflection. Then, the ‘image conditions’ are developed to reduce the number of unknowns by expressing the unknown expansion coefficients of image scattered fields in terms of real counterparts. Use of image conditions, therefore, leads to the \u0000<tex>$4n^2$</tex>\u0000-fold reduction in the size of a matrix for direct solvers and \u0000<tex>$2n$</tex>\u0000-times faster computation in building the system of linear equations than the approach without using them. Multiple scattering models using image conditions are formulated for rigid, pressure release and fluid ellipses under either plane- or cylindrical-wave incidence, and are numerically validated by the boundary element method. Furthermore, potential applications are presented: arrays of elliptically shaped scatterers make in situ tunable noise barriers by rotating scatterers. Finally, polar-coordinate image conditions (for circular objects) are also discussed when coordinates local to circles are also rotated. In Appendix, analytic formulae are provided, which permits the elliptical-coordinate addition theorems used in this article to be calculated by summation instead of numerical integration.","PeriodicalId":92460,"journal":{"name":"The quarterly journal of mechanics and applied mathematics","volume":"73 1","pages":"142-175"},"PeriodicalIF":0.0,"publicationDate":"2020-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qjmam/hbaa005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45211780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0