16,353 research outputs found

    Large-eddy simulation of flows past a flapping airfoil using immersed boundary method

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    The numerical simulation of flows past flapping foils at moderate Reynolds numbers presents two challenges to computational fluid dynamics: turbulent flows and moving boundaries. The direct forcing immersed boundary (IB) method has been developed to simulate laminar flows. However, its performance in simulating turbulent flows and transitional flows with moving boundaries has not been fully evaluated. In the present work, we use the IB method to simulate fully developed turbulent channel flows and transitional flows past a stationary/plunging SD7003 airfoil. To suppress the non-physical force oscillations in the plunging case, we use the smoothed discrete delta function for interpolation in the IB method. The results of the present work demonstrate that the IB method can be used to simulate turbulent flows and transitional flows with moving boundaries

    Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation

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    Mathematical modelling provides a useful framework within which to investigate the organization of biological tissues. With advances in experimental biology leading to increasingly detailed descriptions of cellular behavior, models that consider cells as individual objects are becoming a common tool to study how processes at the single-cell level affect collective dynamics and determine tissue size, shape, and function. However, there often remains no comprehensive account of these models, their method of solution, computational implementation, or analysis of parameter scaling, hindering our ability to utilize and accurately compare different models. Here we present an efficient, open-source implementation of the immersed boundary (IB) method, tailored to simulate the dynamics of cell populations. This approach considers the dynamics of elastic membranes, representing cell boundaries, immersed in a viscous Newtonian fluid. The IB method enables complex and emergent cell shape dynamics, spatially heterogeneous cell properties, and precise control of growth mechanisms. We solve the model numerically using an established algorithm, based on the fast Fourier transform, providing full details of all technical aspects of our implementation. The implementation is undertaken within Chaste, an open-source C++ library that allows one to easily change constitutive assumptions. Our implementation scales linearly with time step, and subquadratically with mesh spacing and immersed boundary node spacing. We identify the relationship between the immersed boundary node spacing and fluid mesh spacing required to ensure fluid volume conservation within immersed boundaries, and the scaling of cell membrane stiffness and cell-cell interaction strength required when refining the immersed boundary discretization. Finally, we present a simulation study of a growing epithelial tissue to demonstrate the applicability of our implementation to relevant biological questions, highlighting several features of the IB method that make it well suited to address certain questions in epithelial morphogenesis

    An immersed boundary-lattice Boltzmann method for single- and multi-component fluid flows

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    International audienceThe paper presents a numerical method to simulate single-and multi-component fluid flows around moving/deformable solid boundaries, based on the coupling of Immersed Boundary (IB) and Lattice Boltzmann (LB) methods. The fluid domain is simulated with LB method using the single relaxation time BGK model, in which an interparticle potential model is applied for multi-component fluid flows. The IB-related force is directly calculated with the interpolated definition of the fluid macroscopic velocity on the Lagrangian points that define the immersed solid boundary. The present IB-LB method can better ensure the no-slip solid boundary condition, thanks to an improved spreading operator. The proposed method is validated through several 2D/3D single-and multi-component fluid test cases with a particular emphasis on wetting conditions on solid wall. Finally, a 3D two-fluid application case is given to show the feasibility of modeling the fluid transport via a cluster of beating cilia

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

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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

    An Immersed Boundary method with divergence-free velocity interpolation and force spreading

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    The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an Eulerian representation of the fluid and a Lagrangian representation of the structure. The Lagrangian and Eulerian frames are coupled by integral transforms with delta function kernels. The discretized IB equations use approximations to these transforms with regularized delta function kernels to interpolate the fluid velocity to the structure, and to spread structural forces to the fluid. It is well-known that the conventional IB method can suffer from poor volume conservation since the interpolated Lagrangian velocity field is not generally divergence-free, and so this can cause spurious volume changes. In practice, the lack of volume conservation is especially pronounced for cases where there are large pressure differences across thin structural boundaries. The aim of this paper is to greatly reduce the volume error of the IB method by introducing velocity-interpolation and force-spreading schemes with the properties that the interpolated velocity field in which the structure moves is at least C1 and satisfies a continuous divergence-free condition, and that the force-spreading operator is the adjoint of the velocity-interpolation operator. We confirm through numerical experiments in two and three spatial dimensions that this new IB method is able to achieve substantial improvement in volume conservation compared to other existing IB methods, at the expense of a modest increase in the computational cost. Further, the new method provides smoother Lagrangian forces (tractions) than traditional IB methods. The method presented here is restricted to periodic computational domains. Its generalization to non-periodic domains is important future work.Comment: 49 pages, 13 figure

    Implicit temperature-correction-based immersed-boundary thermal lattice Boltzmann method for the simulation of natural convection

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    In the present paper, we apply the implicit-correction method to the immersed-boundary thermal lattice Boltzmann method (IB-TLBM) for the natural convection between two concentric horizontal cylinders and in a square enclosure containing a circular cylinder. The Chapman-Enskog multiscale expansion proves the existence of an extra term in the temperature equation from the source term of the kinetic equation. In order to eliminate the extra term, we redefine the temperature and the source term in the lattice Boltzmann equation. When the relaxation time is less than unity, the new definition of the temperature and source term enhances the accuracy of the thermal lattice Boltzmann method. The implicit-correction method is required in order to calculate the thermal interaction between a fluid and a rigid solid using the redefined temperature. Simulation of the heat conduction between two concentric cylinders indicates that the error at each boundary point of the proposed IB-TLBM is reduced by the increment of the number of Lagrangian points constituting the boundaries. We derive the theoretical relation between a temperature slip at the boundary and the relaxation time and demonstrate that the IB-TLBM requires a small relaxation time in order to avoid temperature distortion around the immersed boundary. The streamline, isotherms, and average Nusselt number calculated by the proposed method agree well with those of previous numerical studies involving natural convection. The proposed IB-TLBM improves the accuracy of the boundary conditions for the temperature and velocity using an adequate discrete area for each of the Lagrangian nodes and reduces the penetration of the streamline on the surface of the body

    An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver

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    We propose an efficient algorithm for the immersed boundary method on distributed-memory architectures, with the computational complexity of a completely explicit method and excellent parallel scaling. The algorithm utilizes the pseudo-compressibility method recently proposed by Guermond and Minev [Comptes Rendus Mathematique, 348:581-585, 2010] that uses a directional splitting strategy to discretize the incompressible Navier-Stokes equations, thereby reducing the linear systems to a series of one-dimensional tridiagonal systems. We perform numerical simulations of several fluid-structure interaction problems in two and three dimensions and study the accuracy and convergence rates of the proposed algorithm. For these problems, we compare the proposed algorithm against other second-order projection-based fluid solvers. Lastly, the strong and weak scaling properties of the proposed algorithm are investigated
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