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‣ A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

RANGARAJAN, Ramsharan; LEW, Adrian; BUSCAGLIA, Gustavo C.
Fonte: ELSEVIER SCIENCE SA Publicador: ELSEVIER SCIENCE SA
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.; Stanford Graduate Fellowship; Stanford Graduate Fellowship; Department of the Army Research; Department of the Army Research[W911NF-07-2-0027]; National Institutes of Health (NIH)[U54GM072970]; U.S. National Institutes of Health (NIH); NSF[CMMI-0747089]; U.S. National Science Foundation (NSF); ONR; ONR[N000140810852]; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP (Brasil); CNPq (Brasil); Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

‣ A discontinuous-Galerkin-based immersed boundary method

LEW, Adrian J.; BUSCAGLIA, Gustavo C.
Fonte: JOHN WILEY & SONS LTD Publicador: JOHN WILEY & SONS LTD
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.; PICT[2005-33840]; PICT; NIH[U54 GM072970]; U.S. National Institutes of Health (NIH)

‣ Métodos de fronteira imersa em mecânica dos fluidos; Immersed boundary methods in fluid mechanics

Petri, Larissa Alves
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 24/03/2010 Português
Relevância na Pesquisa
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No desenvolvimento de códigos paralelos, a biblioteca PETSc se destaca como uma ferramenta prática e útil. Com o uso desta ferramenta, este trabalho apresenta um estudo sobre resolvedores de sistemas lineares aplicados a escoamentos incompressíveis de fluidos em microescala, além de uma análise de seu comportamento em paralelo. Após um estudo dos diversos aspectos dos métodos de fronteira imersa, é apresentado um método de fronteira imersa paralelo de primeira ordem. Na sequência, é apresentada uma proposta de melhoria na precisão do método, baseada na minimização da distância entre a condição de contorno exata e aproximada, no sentido de mínimos quadrados. O desenvolvimento de uma ferramenta paralela eficiente é demonstrado na solução numérica de problemas envolvendo escoamentos incompressíveis de fluidos viscosos com fronteiras imersas; In the development of parallel codes, PETSc library has an important position as a practical and useful tool. With this tool, this work presents a study about linear system solvers applied to incompressible flow in microscale problems, furthermore an analysis of the parallel behavior of these methods is presented. After a study of several aspects of immersed boundary methods...

‣ Simulation of the flow through automatic valves of hermetic compressors by the immersed boundary method approach

Rodrigues, T. T.; Gasche, J. L.
Fonte: Universidade Estadual Paulista Publicador: Universidade Estadual Paulista
Tipo: Conferência ou Objeto de Conferência Formato: 181-189
Português
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The main goal of the present work is to verify the applicability of the Immersed Boundary Method together with the Virtual Physical Model to solve the flow through automatic valves of hermetic compressors. The valve was simplified to a two-dimensional radial diffuser, with diameter ratio of D/d = 1.5, and simulated for a one cycle of opening and closing process with a imposed velocity of 3.0 cm/s for the reed, dimensionless gap between disks in the range of 0.07 < s/d < 0.10, and inlet Reynolds number equal to 1500. The good results obtained showed that the methodology has great potential as project tool for this type of valve systems. © The Authors, 2011.

‣ A Sharp-Interface Immersed Boundary Method with Improved Mass Conservation and Reduced Spurious Pressure Oscillations

Seo, Jung Hee; Mittal, Rajat
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 10/08/2011 Português
Relevância na Pesquisa
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A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed. By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric conservation. In order to limit the complexity associated with the cut-cell method, the cut-cell based discretization is limited only to the pressure Poisson and velocity correction equations in the fractional-step method and the small-cell problem tackled by introducing a virtual cell-merging technique. The method is shown to retain all the desirable properties of the original finite-difference based IBM while at the same time, reducing pressure oscillations for moving boundaries by roughly an order of magnitude.

‣ An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods

Li, Zhilin; Song, Peng
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy.

‣ A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

Borazjani, Iman; Ge, Liang; Le, Trung; Sotiropoulos, Fotis
Fonte: PubMed Publicador: PubMed
Tipo: Artigo de Revista Científica
Publicado em 01/04/2013 Português
Relevância na Pesquisa
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We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, Journal of Computational Physics, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data...

‣ Physics and learning based computational models for breaking bow waves based on new boundary immersion approaches

Weymouth, Gabriel David
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 219 p.
Português
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A ship moving on the free surface produces energetic breaking bow waves which generate spray and air entrainment. Present experimental, analytic, and numerical studies of this problem are costly, inaccurate and not robust. This thesis presents new cost-effective and accurate computational tools for the design and analysis of such ocean systems through a combination of physics-based and learning-based models. Methods which immerse physical boundaries on Cartesian background grids can model complex topologies and are well suited to study breaking bow waves. However, current methods such as Volume of Fluid and Immersed Boundary methods have numerical and modeling limitations. This thesis advances the state of the art in Cartesian-grid methods through development of a new conservative Volume-of-fluid algorithm and the Boundary Data Immersion Method, a new approach to the formulation and implementation of immersed bodies. The new methods are simple, robust and shown to out perform existing approaches for a wide range of canonical test problems relevant to ship wave flows. The new approach is used to study breaking bow waves through 2D+T and 3D simulations. The 2D+T computations compare well with experiments and breaking bow wave metrics are shown to be highly sensitive to the ship geometry. 2D+T breaking bow wave predictions are compared quantitatively to 3D computations and shown to be accurate only for certain flow features and very slender high speed vessels. Finally the thesis formalizes the study and development of physics-based learning models (PBLM) for complex engineering systems. A new generalized PBLM architecture is developed based on combining fast simple physics-based models with available high-fidelity data.; (cont.) Models are developed and trained to accurately predict the wave field and breaking bow waves of a ship orders of magnitude faster than standard methods. Built on the new boundary immersion approaches...

‣ Simulação de escoamentos não-periódicos utilizando as metodologias pseudo-espectral e da fronteira imersa acopladas; Simulation of non-periodics flows using the fourier pseudo-spectral and immersed boundary methods

Mariano, Felipe Pamplona
Fonte: Universidade Federal de Uberlândia Publicador: Universidade Federal de Uberlândia
Tipo: Dissertação
Português
Relevância na Pesquisa
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Para compreender fenômenos relacionados à combustão, aeroacústica, transição a turbulência entre outros, a Dinâmica de Fluídos Computacional (CFD) utiliza os métodos de alta ordem. Um dos mais conhecidos é o método pseudo-espectral de Fourier, o qual alia: alta ordem de precisão na resolução das equações, com um baixo custo computacional. Este está ligado à utilização da FFT e do método da projeção do termo da pressão, o qual desvincula os cálculos da pressão da resolução das equações de Navier-Stokes. O procedimento de calcular o campo de pressão, normalmente é o mais oneroso nas metodologias convencionais. Apesar destas vantagens, o método pseudo-espectral de Fourier só pode ser utilizado para resolver problemas com condições de contorno periódicas, limitando o seu uso no campo da dinâmica de fluídos. Visando resolver essa restrição uma nova metodologia é proposta no presente trabalho, que tem como objetivo simular escoamentos não-periódicos utilizando o método pseudo-espectral de Fourier. Para isso, é utilizada a metodologia da Fronteira Imersa, a qual representa as condições de contorno de um escoamento através de um campo de força imposto nas equações de Navier-Stokes. Como teste...

‣ Método da fronteira imersa aplicado à modelagem matemática e simulação numérica de escoamentos turbulentos sobre geometrias móveis e deformáveis; Immersed boundary method applied to mathematical modeling and numerical simulation of turbulent flow over moving and deformable boundaries

Oliveira, José Eduardo Santos
Fonte: Universidade Federal de Uberlândia Publicador: Universidade Federal de Uberlândia
Tipo: Tese de Doutorado
Português
Relevância na Pesquisa
88.9822%
A modelagem matemática de escoamentos turbulentos sobre geometrias complexas móveis possui uma extensa área de aplicações práticas e por isso ocupa lugar de destaque nas pesquisas recentes em engenharia. Uma linha proposta para o tratamento numérico deste tipo de problemas são os métodos de fronteira imersa. Esta metodologia, ainda em desenvolvimento, tem por base a separação do problema em dois domínios distintos, um domínio fixo euleriano utilizado para discretizar as equações do fluido e outro lagrangiano usado para representação da interface fluido-sólido. Como os domínios são geometricamente independentes, não existem restrições quanto à movimentação ou deformação de corpos imersos no escoamento. O presente trabalho apresenta uma extensão do Modelo Físico Virtual, uma metodologia de fronteira imersa desenvolvida no LTCM/UFU, para a simulação de escoamentos a altos números de Reynolds sobre geometrias móveis ou deformáveis. O modelo foi utilizado na simulação de escoamentos laminares sobre corpos deformáveis, aplicados a problemas de otimização de forma. Foram também simulados aerofólios NACA 0012 móveis imersos em escoamentos turbulentos. Um estudo comparativo de três diferentes metodologias de modelagem da turbulência em conjunto com o método de fronteira imersa foi também realizado. São apresentados resultados dos coeficientes de arrasto...

‣ Modelagem matemática tridimensional para problemas de interação fluido-estrutura; Mathematical modeling for three-dimensional fluid-structure interaction problems

Campregher Junior, Rubens
Fonte: Universidade Federal de Uberlândia Publicador: Universidade Federal de Uberlândia
Tipo: Tese de Doutorado
Português
Relevância na Pesquisa
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A modelagem matemática e a simulação numérica de escoamentos turbulentos tridimensionais ao redor de geometrias complexas móveis constituem um dos grandes desafios da engenharia moderna. A discretização de domínios tridimensionais costuma exigir grande capacidade de armazenamento e processamento de dados que, se somados aos freqüentes refinamentos locais das malhas, torna os cálculos extremamente caros. Por sua vez, a representação de geometrias complexas empregando coordenadas generalizadas, pode gerar dificuldades matemáticas ou numéricas, além de possuírem abrangência limitada. A metodologia de Fronteira Imersa está sendo desenvolvida como uma alternativa para lidar com este problema, separando-o em dois domínios distintos: um domínio lagrangiano para representar a interface sólido/fluido e um domínio euleriano para discretizar o fluido. O presente trabalho apresenta uma extensão para problemas tridimensionais de uma metodologia de fronteira imersa, desenvolvida no LTCM, denominada Modelo Físico Virtual. O domínio euleriano foi discretizado com aproximações espaciais e temporais de segunda ordem, empregando Volumes Finitos em malhas cartesianas e com capacidade de processamento paralelo. O domínio lagrangiano foi construído com uma malha de elementos triangulares. Os testes preliminares foram feitos de forma a validar...

‣ Immersed boundary methods with applications to flow control

Kellogg, Steven Michael
Fonte: Universidade Rice Publicador: Universidade Rice
Português
Relevância na Pesquisa
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While some engineers use computers as a first line of attack on design problems, others are persistently making computers and their software faster and more capable of solving realistic problems. The technology used to build the microscale electronic components that makes computers fast is also used to construct micron-scale electromechanical (MEMS) actuators ideal for use in control schemes to reduce drag in industrial flows, promising millions of dollars in cost savings. The Immersed Boundary Condition (IBC) developed here augments a common fractional step, pseudospectral method used with Large Eddy Simulation to inexpensively and more realistically simulate turbulent flow over MEMS-like actuators. This is done by augmenting the numerical method to simulate flow over unsteady, irregular boundaries with static, structured rectilinear grids. The method is validated and applied to evaluate actuator characteristics and simulate open and closed loop flow control with continuous and discrete, MEMS-like actuators.

‣ An Improved Immersed-Boundary Algorithm for Fluid-Solid Interaction un Lattice-Boltzmann Simulations

Boroni, Gustavo Adolfo; Dottori, Javier Alejandro; Dalponte, Diego David; Rinaldi, Pablo Rafael; Clausse, Alejandro
Fonte: Plapiqui (uns-conicet) Publicador: Plapiqui (uns-conicet)
Tipo: info:eu-repo/semantics/article; info:ar-repo/semantics/artículo; info:eu-repo/semantics/publishedVersion Formato: application/pdf
Português
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An improved algorithm combining the features of the lattice Boltzmann and the immersed-boundary methods is presented. Following previous formulations, the method represents a fluid con-strained by flexible boundaries by means of a force term acting on the cells adjacent to the boundary, which in turn is moved by the fluid. The present al-gorithm introduces a more efficient iteration proce-dure to calculate the fluid-boundary interaction, which facilitates the implementation. The simulations where validated against experimental and analytical data showing good agreement and demonstrating the performance of the method to simulate different kind of fluid-solid interaction; Fil: Boroni, Gustavo Adolfo. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados; Argentina;; Fil: Dottori, Javier Alejandro. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados; Argentina;; Fil: Dalponte, Diego David. Comisión Nacional de Energía Atómica, Argentina.;; Fil: Rinaldi, Pablo Rafael. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Grupo de Plasmas Densos Magnetizados; Argentina;; Fil: Clausse...

‣ A Study of Different Modeling Choices For Simulating Platelets Within the Immersed Boundary Method

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, R. M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/10/2012 Português
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The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise-linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations - radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations - for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise-linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations.; Comment: 33 pages...

‣ Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review

Schneider, Kai
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/08/2015 Português
Relevância na Pesquisa
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Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.; Comment: in Journal of Plasma Physics, 2015

‣ Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

Stein, David B.; Guy, Robert D.; Thomases, Becca
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.

‣ Removing the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations

Hou, Thomas Y.; Shi, Zuoqiang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
48.6436%
The Immersed Boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semi-implicit schemes to remove this stiffness from the Immersed Boundary method for the two-dimensional Stokes flow. First, we obtain a novel unconditionally stable semi-implicit discretization for the immersed boundary problem. Using this unconditionally stable discretization as a building block, we derive several efficient semi-implicit schemes for the immersed boundary problem by applying the Small Scale Decomposition to this unconditionally stable discretization. Our stability analysis and extensive numerical experiments show that our semi-implicit schemes offer much better stability property than the explicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit schemes can be solved explicitly in the spectral space. Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme, but with a much better stability property.; Comment: 40 pages with 8 figures

‣ An Immersed Boundary Fourier Pseudo-spectral Method for Simulation of Confined Two-dimensional Incompressible Flows

Sabetghadam, Fereidoun; Badri, Mehdi; Sharafatmandjoor, Shervin; Kor, Hosnieh
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/10/2011 Português
Relevância na Pesquisa
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The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier--Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to many other similar methods, there is not an explicit external forcing function in the present formulation. The desired immersed boundary conditions are approximated on some regular grid points, using different orders (up to second-order) polynomial extrapolations. At the beginning of each timestep, the solenoidal velocities (also satisfying the desired immersed boundary conditions), are obtained and fed into a conventional pseudo-spectral solver, together with a modified vorticity. The zero-mean pseudo-spectral solution is employed, and therefore, the method is applicable to the confined flows with zero mean velocity and vorticity, and without mean vorticity dynamics. In comparison to the classical Fourier pseudo-spectral solution, the method needs ${\cal O}(4(1+\log N)N)$ more operations for boundary condition settings. Therefore, the computational cost of the method, as a whole...

‣ An efficient semi-implicit immersed boundary method for the Navier–Stokes equations

Hou, T. Y.; Shi, Z.
Fonte: Elsevier Publicador: Elsevier
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em 20/10/2008 Português
Relevância na Pesquisa
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The immersed boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability constraint, but none of them give satisfactory performance. In this paper, we propose an efficient semi-implicit scheme to remove this stiffness from the immersed boundary method for the Navier–Stokes equations. The construction of our semi-implicit scheme consists of two steps. First, we obtain a semi-implicit discretization which is proved to be unconditionally stable. This unconditionally stable semi-implicit scheme is still quite expensive to implement in practice. Next, we apply the small scale decomposition to the unconditionally stable semi-implicit scheme to construct our efficient semi-implicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit scheme can be solved explicitly in the spectral space. Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme. Our extensive numerical experiments show that our semi-implicit scheme has much better stability property than an explicit scheme. This offers a substantial computational saving in using the immersed boundary method.

‣ RRemoving the Stiffness of Elastic Force from the Immersed Boundary Method for the 2D Stokes Equations

Hou, Thomas Y.; Shi, Zuoqiang
Fonte: Elsevier Publicador: Elsevier
Tipo: Article; PeerReviewed Formato: application/pdf
Publicado em 10/11/2008 Português
Relevância na Pesquisa
48.6436%
The immersed boundary method has evolved into one of the most useful computational methods in studying fluid structure interaction. On the other hand, the immersed boundary method is also known to suffer from a severe timestep stability restriction when using an explicit time discretization. In this paper, we propose several efficient semi-implicit schemes to remove this stiffness from the immersed boundary method for the two-dimensional Stokes flow. First, we obtain a novel unconditionally stable semi-implicit discretization for the immersed boundary problem. Using this unconditionally stable discretization as a building block, we derive several efficient semi-implicit schemes for the immersed boundary problem by applying the small scale decomposition to this unconditionally stable discretization. Our stability analysis and extensive numerical experiments show that our semi-implicit schemes offer much better stability property than the explicit scheme. Unlike other implicit or semi-implicit schemes proposed in the literature, our semi-implicit schemes can be solved explicitly in the spectral space. Thus the computational cost of our semi-implicit schemes is comparable to that of an explicit scheme, but with a much better stability property.