Boundary Element Methods

Kythe, Prem K.

doi:10.1007/978-1-4612-4106-5_11

Cited by 26 publications

(21 citation statements)

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“…The compact support of node I is chosen to be the union of element domains attached to node I as with standard finite elements. Let this domain be denoted by Ω I with boundary Γ I and outward unit normal n. The nodal weight function is defined as the solution to the following auxiliary Poisson problem, This auxiliary problem may be efficiently solved using standard boundary element techniques [34] to obtain the value of the weight function and its derivatives at the Voronoi cell integration points x j , j = 1, …, M, although in the two-dimensional example problem given in Section 6 the finite element method was used. Eqs.…”

Section: Polyhedral Element Formulationmentioning

confidence: 99%

Simulating the pervasive fracture and fragmentation of materials and structures using randomly close-packed Voronoi tessellations.

Bishop¹

2008

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Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. Two primary applications in which pervasive fracture is encountered are (1) weapons effects on structures and (2) geomechanics of highly jointed and faulted reservoirs.A pure Lagrangian computational method based on randomly close-packed Voronoi tessellations is proposed as a rational approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the reproducing kernel method. Fracture surfaces are allowed to nucleate only at the intercell faces. The randomly seeded Voronoi cells provide an unbiased network for representing cracks. In this initial study two approaches for allowing the new surfaces to initiate are studied: (1) dynamic mesh connectivity and the instantaneous insertion of a cohesive traction when localization is detected, and (2) a discontinuous Galerkin approach in which the interelement tractions are an integral part of the variational formulation, but only become active once localization is detected.Pervasive fracture problems are extremely sensitive to initial conditions and system parameters. Dynamic problems exhibit a form of transient chaos. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest.3

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Section: Polyhedral Element Formulationmentioning

confidence: 99%

Simulating the pervasive fracture and fragmentation of materials and structures using randomly close-packed Voronoi tessellations.

Bishop¹

2008

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“…Many classic numerical methods such as the finite difference method (FDM) [1], the finite element method (FEM) [2], and the boundary element method (BEM) [3], and other modified methods [4,5] have been applied in spectral or temporal acoustic simulations. In particular, meshfree methods are widely applied to solve acoustics problems, because field points used in this method are arbitrarily distributed and the approximation smoothness order is chosen flexibility.…”

Section: Introductionmentioning

confidence: 99%

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

Zhang

2017

Preprint

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Abstract:The development of computational acoustics allows simulation of sound generation and propagation in complex environment. In particular, meshfree methods are widely used to solve acoustics problems through arbitrarily distributed field points and approximation smoothness flexibility. As a Lagrangian meshfree method, smoothed particle hydrodynamics (SPH) method reduce the difficulty in solving problems with deformable boundaries, complex topologies, or multiphase medium. The traditional SPH method has been applied in acoustic simulation. This study presents the corrective smoothed particle method (CSPM), which is a combination of SPH kernel estimate and Taylor series expansion. The CSPM is introduced as a Lagrangian approach to improve accuracy in solving acoustic wave equations in the time domain. Moreover, a boundary treatment technique based on the hybrid meshfree and finite difference time domain (FDTD) method is proposed to represent different acoustic boundaries with particles. To model sound propagation in pipes with different boundaries, soft, rigid, and absorbing boundary conditions are built with this technique. Numerical results show that the CSPM algorithm is consistent and demonstrates convergence with exact solutions. Main computational parameters are discussed, and different boundary conditions are validated to be effective for benchmark problems in computational acoustics.

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“…Eulerian approaches have mainly been used to implement numerical approximations to these models, and different numerical methods include the finite difference method (FDM) [11], the finite element method (FEM) [12], the boundary element method (BEM) [13], and other modified or coupled methods [14][15][16]. These methods have shown their power in solving various acoustic problems so far.…”

Section: Introductionmentioning

confidence: 99%

A Lagrangian Approach for Computational Acoustics with Meshfree Method

Zhang

Smith

Zhang

et al. 2017

Preprint

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Abstract:Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

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Boundary Element Methods

Cited by 26 publications

References 0 publications

Simulating the pervasive fracture and fragmentation of materials and structures using randomly close-packed Voronoi tessellations.

Simulating the pervasive fracture and fragmentation of materials and structures using randomly close-packed Voronoi tessellations.

Modeling Sound Propagation Using the Corrective Smoothed Particle Method with an Acoustic Boundary Treatment Technique

A Lagrangian Approach for Computational Acoustics with Meshfree Method

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