Boundary Integral Equation Model Research Articles

Momentum Conservative Scheme for Simulating Wave Runup and Underwater Landslide

This paper focuses on the numerical modelling and simulation of tsunami waves triggered by an underwater landslide. The equation of motion for water waves is represented by the Nonlinear Shallow Water Equations (NSWE). Meanwhile, the motion of underwater landslide is modeled by incorporating a term for bottom motion into the NSWE. The model is solved numerically by using a finite volume method with a momentum conservative staggered grid scheme that is proposed by Stelling & Duinmeijer 2003 [12]. Here, we modify the scheme for the implementation of bottom motion. The accuracy of the implementation for representing wave runup and rundown is shown by performing the runup of harmonic wave as proposed by Carrier & Greenspan 1958 [2], and also solitary wave runup of Synolakis, 1986 [14], for both breaking and non-breaking cases. For the underwater landslide, result of the simulation is compared with simulation using the Boundary Integral Equation Model (BIEM) that is performed by Lynett and Liu, 2002 [9].

Application of boundary integral equations for analyzing the dynamics of elastic, viscoelastic, and poroelastic bodies

Two approaches (classical and nonclassical) of the boundary integral equation method for solving three-dimensional dynamical boundary value problems of elasticity, viscoelasticity, and poroelasticity are considered. The boundary integral equation model is used for porous materials. The Kelvin–Voigt model and the weakly singular hereditary Abel kernel are used to describe the viscoelastic properties. Both approaches permit solving the dynamic problems exactly not only in the isotropic but also in the anisotropic case. The boundary integral equation solution scheme is constructed on the basis of the boundary element technique. The numerical results obtained by the classical and nonclassical approaches are compared.

Computing transverse elasticity modulus of composites using boundary integral equation method

Abstract In this study, the boundary integral equation (BIE) method is presented for the prediction of the transverse elasticity modulus of composites. The details of the BIE model covering infinite friction (stick) contact conditions are given. Both fiber and matrix materials are assumed to display linear elastic material behavior. The formulation is applied to four composite samples, e-glass/epoxy, s-glass/epoxy, boron/epoxy, and T300/epoxy. It is shown that the computed results are in very good agreement with the Tsai-Hahn equation.

Design Oriented Aerodynamic Modelling of Wind Turbine Performance

The development of a wind turbine aerodynamics model using a Boundary Integral Equation model (BIEM) is presented. The methodology is valid to study inviscid unsteady flows around three dimensional bodies of arbitrary shape and arbitrarily moving with respect to the incoming flow. The extension of this methodology to study viscosity effects in turbine blade flow at high angle of attack is addressed and an approach to determine aerodynamic loads over a wide range of turbine operating conditions is proposed. Numerical applications considering a selected test cases from the NREL experimental dataset are presented. Finally, the application of the proposed turbine aerodynamics model into a multi-disciplinary study including aeroelasticity of pylon-turbine assembly and aeroacoustics modelling of induced noise is briefly described.

Role of geomorphic and hydraulic parameters in governing pore water seepage from salt marsh sediments

A numerical boundary integral equation model has been used to study the effects of marsh geomorphology and hydraulic parameters on the seepage of pore water into tidal channels and its subsequent recharge by tidal inundation. In general, the results show that regardless of the geomorphic configuration the locus of maximum seepage flux occurs at or near the intersection of the creek bank and the channel water surface. Over a tidal cycle, typically two thirds of the total seepage discharge occurs through the creek bank with only about a third discharging from the channel bottom. In most cases the volume of seepage discharging through the creek bank exceeds by a factor of two or more that emanating from the channel bottom. Of the creek bank discharge, up to half may occur through the seepage face that develops above the tide line at tidal stages below mean tide. The ratio of creek bank to bottom seepage only approaches unity when the thickness of the aquifer beneath the bottom is similar to or greater than the width of the channel bottom and the ratio of conductivity to specific yield exceeds 0.5. For given hydraulic parameters, total seepage volume varies directly with creek bank slope and aquifer thickness, whereas these factors are inversely related to the ratio of the two seepage components. Channel bottom width, on the other hand, has no influence on total seepage volume but greatly increases the component ratio as the width approaches zero. Since most of the seepage discharge is derived from sediments within several meters of the creek bank, variations in seepage discharge driven by variations in marsh geomorphology might play a role in the productivity of creekside cord grass. Several hypotheses are offered and discussed regarding the effects of geomorphology on creekside productivity. These results also indicate that placement of seepage meters only on the channel bottom will not give samples or measures representative of the total seepage.

Dynamic Slip Transfer from the Denali to Totschunda Faults, Alaska: Testing Theory for Fault Branching

We analyze the observed dynamic slip transfer from the Denali to Totschunda faults during the Mw 7.9 3 November 2002 Denali fault earthquake, Alaska. This study adopts the theory and methodology of Poliakov et al. (2002) and Kame et al. (2003), in which it was shown that the propensity of the rupture path to follow a fault branch is determined by the preexisting stress state, branch angle, and incoming rupture velocity at the branch location. Here we check that theory on the DenaliTotschunda rupture process using 2D numerical simulations of processes in the vicinity of the branch junction. The maximum compression direction with respect to the strike of the Denali fault near the junction has been estimated to range from approximately 73 to 80. We use the values of 70 and 80 in our numerical simulations. The rupture velocity at branching is not well constrained but has been estimated to average about 0.8 cs throughout the event. We use 0.6 cs, 0.8 cs, 0.9 cs, and even 1.4 cs as parameters in our simulations. We simulate slip transfer by a 2D elastodynamic boundary integral equation model of mode II slip-weakening rupture with self-chosen path along the branched fault system. All our simulations except for 70 and 0.9 cs predict that the rupture path branches off along the Totschunda fault without continuation along the Denali fault. In that exceptional case there is also continuation of rupture along the Denali fault at a speed slower than that along the Totschunda fault and with smaller slip.

A modeling study of the dynamics of pore water seepage from intertidal marsh sediments

A numerical boundary integral equation model has been used to simulate tidally driven transient variations in pore water seepage from salt marsh sediments into tidal channels and its subsequent recharge by tidal inundation. In general the results show that the maximum seepage discharge occurs at or near the intersection of the creek bank and the channel water surface. Over a tidal cycle typically two-thirds of the total seepage discharge occurs through the creek bank with only about a third discharging from the channel bottom. Of the creek-bank discharge up to a third occurs through the seepage face that develops above the tide line at tidal stages below mean tide. These results indicate that placement of seepage meters only on the channel bottom will not give samples or measures representative of the total seepage. Of the total recharge only about 5% occurs through the upper part of the creek bank with the remainder infiltrating vertically through the marsh platform during early stages of tidal submergence. For the platform recharge about 80% occurs within 3 m of the creek bank. Thus, most of the water that seeps out of marsh sediments is derived from sediments that lie within several meters of the creek bank and accordingly has had a relatively short residence (one to two years) in the marsh. Compared to the distal portion of the marsh this relatively rapid flushing may enhance the productivity of Spartina alterniflora in the creek-bank environment and control the differential generation of radium quartet isotopes.

The Riemann complex boundary element method for the solutions of two-dimensional Elliptic equations

In this paper, a new boundary integral equation model Riemann complex boundary element method (RCBEM), is proposed based on the boundary element method (BEM) and the theory of Vekua and its modification as well as complex Riemann function as the fundamental solution. The RCBEM method is used to solve the linear, second order, elliptical partial differential equations in the fluid flow problems. In comparison to the generally used BEM, for RCBEM, there are two distinct differences. First one is that, RCBEM applies complex Riemann function as the fundamental solution of the adjoint operator while in direct BEM, on the other hand Green function is used. The second one is that the governing equations should be transformed into complex domain because there exist two characteristics in complex plane for elliptic systems, while in the direct BEM is not, since the Green function is adopted instead. The singular problem occurring in direct BEM can be avoided in RCBEM, especially for regular domain problems. The efficiency and accuracy of the RCBEM depends on the complex variable integration. To verify the feasibility and accuracy of RCBEM, the model is applied to different case studies of potential flows, Helmholtz equation problem and advection–diffusion problem and results are compared with analytical solutions and other numerical models. The results are satisfactory and prove the applicability of RCBEM for various two-dimensional elliptic equation problems.

Hydrodynamic pressures acting on rigid gravity dams during earthquakes

A boundary integral equation model is developed based on the analytical integrals for three-dimensional potential problems. All necessary integrals are first converted into line integrals around a target element and then integrated analytically. The developed model is applied to a practical problem concerning computation of the hydrodynamic pressure acting on a dam face of a dam-reservoir system during earthquakes. The obtained numerical solutions are compared with available two-dimensional experimental data and analytical solutions. A very good agreement is observed. The model is then used to investigate three-dimensional effects of a complex dam-reservoir system.

Layerwise fundamental solutions and three-dimensional model for layered media

A hybrid method is presented for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multilayered system using a total potential energy formulation and employing the layerwise laminate theory of Reddy. The developed boundary integral equation model is two-dimensional, displacement based and assumes piecewise continuous distribution of the displacement components through the system's thickness. A one-dimensional finite element model is used for the analysis of the multilayered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of a typical infinite layer (element), which can be applied in a two-dimensional boundary integral equation model to analyze layered structures. This model describes the three-dimensional displacement field at arbitrary points either in the domain of the layered medium or on its boundary. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems.

A layerwise boundary integral equation model for layers and layered media

A hybrid method is presented for the analysis of layers, plates, and multilayered systems consisting of isotropic and linear elastic materials. The problem is formulated for the general case of a multilayered system using a total potential energy formulation. The layerwise laminate theory of Reddy is employed to develop a layerwise, two-dimensional, displacement-based, hybrid boundary element model that assumes piecewise continuous distribution of the displacement components through the system's thickness. A one-dimensional finite element model is used for the analysis of the multilayered system through its thickness, and integral Fourier transforms are used to obtain the exact solution for the in-plane problem. Explicit expressions are obtained for the fundamental solution of a typical infinite layer (element) assuming linear displacement distribution through its thickness. This fundamental solution is given in a closed form in the cartesian space, and it can be applied in the two-dimensional boundary integral equation model to analyze layered structures with finite dimensions. The proposed method provides a simple, efficient, and versatile model for a three-dimensional analysis of thick plates or multilayered systems.

Elastoplastic BIE analysis of cracked plates and related problems. Part 2: Numerical results

AbstractPart 1 of this paper reports on the formulation of an advanced boundary—integral equation model for fracture mechanics analysis of cracked plates, subject to elastoplastic behaviour or other, related body force problems. The basis of this formulation contrasts with other BIE elastoplastic formulations in the use of the Green's function for an infinite plane containing a stress free crack. This Green's function formulation assures that the total elastic strain field for the crack problem is accurately imbedded in the numerical model. The second part of this paper reports on the numerical implementation of this algorithm, as currently developed. The anelastic strain field (residual strains, thermal strains, plastic strains, etc.) is approximated as piecewise constant, while the boundary data is modelled with linear interpolations. An iteration solution scheme is adopted which eliminates the need for recalculation of the BIE matrices. The stability and accuracy of the algorithm are demonstrated for an uncracked, notch geometry, and comparison to finite element results is made for the centre‐cracked panel. The data shows that even the crude plastic strain model applied is capable of excellent resolution of crack tip plastic behaviour.