934 research outputs found
On Meshfree GFDM Solvers for the Incompressible Navier-Stokes Equations
Meshfree solution schemes for the incompressible Navier--Stokes equations are
usually based on algorithms commonly used in finite volume methods, such as
projection methods, SIMPLE and PISO algorithms. However, drawbacks of these
algorithms that are specific to meshfree methods have often been overlooked. In
this paper, we study the drawbacks of conventionally used meshfree Generalized
Finite Difference Method~(GFDM) schemes for Lagrangian incompressible
Navier-Stokes equations, both operator splitting schemes and monolithic
schemes. The major drawback of most of these schemes is inaccurate local
approximations to the mass conservation condition. Further, we propose a new
modification of a commonly used monolithic scheme that overcomes these problems
and shows a better approximation for the velocity divergence condition. We then
perform a numerical comparison which shows the new monolithic scheme to be more
accurate than existing schemes
Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method
A meshfree Lagrangian method for the fluctuating hydrodynamic equations
(FHEs) with fluid-structure interactions is presented. Brownian motion of the
particle is investigated by direct numerical simulation of the fluctuating
hydrodynamic equations. In this framework a bidirectional coupling has been
introduced between the fluctuating fluid and the solid object. The force
governing the motion of the solid object is solely due to the surrounding fluid
particles. Since a meshfree formulation is used, the method can be extended to
many real applications involving complex fluid flows. A three-dimensional
implementation is presented. In particular, we observe the short and long-time
behaviour of the velocity autocorrelation function (VACF) of Brownian particles
and compare it with the analytical expression. Moreover, the Stokes-Einstein
relation is reproduced to ensure the correct long-time behaviour of Brownian
dynamics.Comment: 24 pages, 2 figure
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