177 research outputs found
A unified operator splitting approach for multi-scale fluid-particle coupling in the lattice Boltzmann method
A unified framework to derive discrete time-marching schemes for coupling of
immersed solid and elastic objects to the lattice Boltzmann method is
presented. Based on operator splitting for the discrete Boltzmann equation,
second-order time-accurate schemes for the immersed boundary method, viscous
force coupling and external boundary force are derived. Furthermore, a modified
formulation of the external boundary force is introduced that leads to a more
accurate no-slip boundary condition. The derivation also reveals that the
coupling methods can be cast into a unified form, and that the immersed
boundary method can be interpreted as the limit of force coupling for vanishing
particle mass. In practice, the ratio between fluid and particle mass
determines the strength of the force transfer in the coupling. The integration
schemes formally improve the accuracy of first-order algorithms that are
commonly employed when coupling immersed objects to a lattice Boltzmann fluid.
It is anticipated that they will also lead to superior long-time stability in
simulations of complex fluids with multiple scales
Lattice Boltzmann model approximated with finite difference expressions
We show that the asymptotic properties of the link-wise artificial
compressibility method are not compatible with a correct approximation of fluid
properties. We propose to adapt the previous method through a framework
suggested by the Taylor expansion method and to replace first order terms in
the expansion by appropriate three or five points finite differences and to add
non linear terms. The "FD-LBM" scheme obtained by this method is tested in two
dimensions for shear wave, Stokes modes and Poiseuille flow. The results are
compared with the usual lattice Boltzmann method in the framework of multiple
relaxation times
Mesoscopic Methods in Engineering and Science
(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics is usually insensitive to the details of the underlying microscopic interactions
High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation
We construct a high order discontinuous Galerkin method for solving general
hyperbolic systems of conservation laws. The method is CFL-less, matrix-free,
has the complexity of an explicit scheme and can be of arbitrary order in space
and time. The construction is based on: (a) the representation of the system of
conservation laws by a kinetic vectorial representation with a stiff relaxation
term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport
solver; and (c) a stiffly accurate composition method for time integration. The
method is validated on several one-dimensional test cases. It is then applied
on two-dimensional and three-dimensional test cases: flow past a cylinder,
magnetohydrodynamics and multifluid sedimentation
Splitting a heart
This thesis investigates and numerically solves the Wohlfart-Arloch equations describing the electrical activity in the atrial part of the heart. This is done through operator splitting that is allowing the diffusion of ionic currents, and the local voltage-driven reactions in each cell to be de-coupled. The local reactions can be solved in closed form, and the diffusion part is solved with a spectral method by interpolating using eigenmodes. The problem of initiating the system is solved by introducing time-dependent boundary conditions and solving these parts as a series. Systematic investigations are carried out both concerning the numerical errors and also the wave speed, multiple pulse shape, and other characteristics relevant to ascertaining the validity of the numerical method used
Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium
This is a continuation of the previous work (Takata & Noguchi, J. Stat.
Phys., 2018) that introduces the presumably simplest model of kinetic theory
for phase transition. Here, main concern is to clarify the stability of uniform
equilibrium states in the kinetic regime, rather than that in the continuum
limit. It is found by the linear stability analysis that the linear neutral
curve is invariant with respect to the Knudsen number, though the transition
process is dependent on the Knudsen number. In addition, numerical computations
of the (nonlinear) kinetic model are performed to investigate the transition
processes in detail. Numerical results show that (unexpected) incomplete
transitions may happen as well as clear phase transitions.Comment: 21 pages, 7 figure
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