5,349 research outputs found
Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review
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, 201
A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions
A new parallel, computationally efficient immersed boundary method for
solving three-dimensional, viscous, incompressible flows on unbounded domains
is presented. Immersed surfaces with prescribed motions are generated using the
interpolation and regularization operators obtained from the discrete delta
function approach of the original (Peskin's) immersed boundary method. Unlike
Peskin's method, boundary forces are regarded as Lagrange multipliers that are
used to satisfy the no-slip condition. The incompressible Navier-Stokes
equations are discretized on an unbounded staggered Cartesian grid and are
solved in a finite number of operations using lattice Green's function
techniques. These techniques are used to automatically enforce the natural
free-space boundary conditions and to implement a novel block-wise adaptive
grid that significantly reduces the run-time cost of solutions by limiting
operations to grid cells in the immediate vicinity and near-wake region of the
immersed surface. These techniques also enable the construction of practical
discrete viscous integrating factors that are used in combination with
specialized half-explicit Runge-Kutta schemes to accurately and efficiently
solve the differential algebraic equations describing the discrete momentum
equation, incompressibility constraint, and no-slip constraint. Linear systems
of equations resulting from the time integration scheme are efficiently solved
using an approximation-free nested projection technique. The algebraic
properties of the discrete operators are used to reduce projection steps to
simple discrete elliptic problems, e.g. discrete Poisson problems, that are
compatible with recent parallel fast multipole methods for difference
equations. Numerical experiments on low-aspect-ratio flat plates and spheres at
Reynolds numbers up to 3,700 are used to verify the accuracy and physical
fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational
Physic
Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library
In this paper we employ two implementations of the fictitious domain (FD)
method to simulate water-entry and water-exit problems and demonstrate their
ability to simulate practical marine engineering problems. In FD methods, the
fluid momentum equation is extended within the solid domain using an additional
body force that constrains the structure velocity to be that of a rigid body.
Using this formulation, a single set of equations is solved over the entire
computational domain. The constraint force is calculated in two distinct ways:
one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method
and another using a fully-Eulerian approach of the Brinkman penalization (BP)
method. Both FSI strategies use the same multiphase flow algorithm that solves
the discrete incompressible Navier-Stokes system in conservative form. A
consistent transport scheme is employed to advect mass and momentum in the
domain, which ensures numerical stability of high density ratio multiphase
flows involved in practical marine engineering applications. Example cases of a
free falling wedge (straight and inclined) and cylinder are simulated, and the
numerical results are compared against benchmark cases in literature.Comment: The current paper builds on arXiv:1901.07892 and re-explains some
parts of it for the reader's convenienc
An efficient parallel immersed boundary algorithm using a pseudo-compressible fluid solver
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
Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry
We develop a volume penalization method for inhomogeneous Neumann boundary
conditions, generalizing the flux-based volume penalization method for
homogeneous Neumann boundary condition proposed by Kadoch et al. [J. Comput.
Phys. 231 (2012) 4365]. The generalized method allows us to model scalar flux
through walls in geometries of complex shape using simple, e.g. Cartesian,
domains for solving the governing equations. We examine the properties of the
method, by considering a one-dimensional Poisson equation with different
Neumann boundary conditions. The penalized Laplace operator is discretized by
second order central finite-differences and interpolation. The discretization
and penalization errors are thus assessed for several test problems.
Convergence properties of the discretized operator and the solution of the
penalized equation are analyzed. The generalized method is then applied to an
advection-diffusion equation coupled with the Navier-Stokes equations in an
annular domain which is immersed in a square domain. The application is
verified by numerical simulation of steady free convection in a concentric
annulus heated through the inner cylinder surface using an extended square
domain.Comment: 32 pages, 19 figure
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