41,061 research outputs found
Hybrid finite difference/finite element immersed boundary method
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian
description of the structural deformations, stresses, and forces along with an Eulerian description of the
momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary
methods described immersed elastic structures using systems of flexible fibers, and even now, most
immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This
work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian
variables that facilitates independent spatial discretizations for the structure and background grid. This
approach employs a finite element discretization of the structure while retaining a finite difference scheme
for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively
contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases
in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors
that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes.
The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse
structural meshes with the immersed boundary method. This work also contrasts two different weak forms
of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations
facilitated by our coupling approach
Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations
After we derive the Serre system of equations of water wave theory from a
generalized variational principle, we present some of its structural
properties. We also propose a robust and accurate finite volume scheme to solve
these equations in one horizontal dimension. The numerical discretization is
validated by comparisons with analytical, experimental data or other numerical
solutions obtained by a highly accurate pseudo-spectral method.Comment: 28 pages, 16 figures, 75 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
Partitioned semi-implicit methods for simulation of biomechanical fluid-structure interaction problems
This article is published under a CC BY licence. The Version of Record is available online at: http://dx.doi.org/10.1088/1742-6596/745/3/032020.This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an
incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we
implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled
explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability.
Several coupling schemes are tested including fixed-point method with different static and dynamic relaxation,
as well as Newton-Krylov method with approximated Jacobian. Numerical tests are conducted in the context of a
biomechanical problem. Results indicate that the Newton-Krylov solver outperforms fixed point ones while introducing
more complexity to the problem due to the evaluation of the Jacobian. Fixed-point solver with Aitken's relaxation
method also proved to be a simple, yet efficient method for FSI simulations.Peer ReviewedPostprint (published version
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
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