235 research outputs found
FluSI: A novel parallel simulation tool for flapping insect flight using a Fourier method with volume penalization
FluSI, a fully parallel open source software for pseudo-spectral simulations
of three-dimensional flapping flight in viscous flows, is presented. It is
freely available for non-commercial use under
[https://github.com/pseudospectators/FLUSI]. The computational framework runs
on high performance computers with distributed memory architectures. The
discretization of the three-dimensional incompressible Navier--Stokes equations
is based on a Fourier pseudo-spectral method with adaptive time stepping. The
complex time varying geometry of insects with rigid flapping wings is handled
with the volume penalization method. The modules characterizing the insect
geometry, the flight mechanics and the wing kinematics are described.
Validation tests for different benchmarks illustrate the efficiency and
precision of the approach. Finally, computations of a model insect in the
turbulent regime demonstrate the versatility of the software
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
Simulation of forced deformable bodies interacting with two-dimensional incompressible flows: Application to fish-like swimming
International audienceWe present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible flows. The temporal and spatial discretizations of the Navier-Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge-Kutta and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body interacting with the surrounding fluid due to the hydrodynamic forces and moment calculated on the Eulerian reference grid. An efficient law for curvature control of an anguilliform fish, swimming to a prescribed goal, is proposed. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems
Development of an adaptive multi-resolution method to study the near wall behavior of two-dimensional vortical flows
In the present investigation, a space-time adaptive multiresolution method is developed to solve evolutionary PDEs, typically encountered in fluid mechanics. The new method is based on a multiresolution analysis which allows to reduce the number of active grid points significantly by refining the grid automatically in regions of steep gradients, while in regions where the solution is smooth coarse grids are used. The method is applied to the one-dimensional Burgers equation as a classical example of nonlinear advection-diffusion problems and then extended to the incompressible two-dimensional Navier-Stokes equations. To study the near wall behavior of two-dimensional vortical flows a recently revived, dipole collision with a straight wall is considered as a benchmark. After that an extension to interactions with curved walls of concave or convex shape is done using the volume penalization method. The space discretization is based on a second order central finite difference method with symmetric stencil over an adaptive grid. The grid adaptation strategy exploits the local regularity of the solution estimated via the wavelet coefficients at a given time step. Nonlinear thresholding of the wavelet coefficients in a one-to-one correspondence with the grid allows to reduce the number of grid points significantly. Then the grid for the next time step is extended by adding a safety zone in wavelet coefficient space around the retained coefficients in space and scale. With the use of Harten's point value multiresolution framework, general boundary conditions can be applied to the equations. For time integration explicit Runge-Kutta methods of different order are implemented, either with fixed or adaptive time stepping. The obtained results show that the CPU time of the adaptive simulations can be significantly reduced with respect to simulations on a regular grid. Nevertheless the accuracy order of the underlying numerical scheme is preserved
Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint
We report the results of a detailed study of the spectral properties of
Laplace and Stokes operators, modified with a volume penalization term designed
to approximate Dirichlet conditions in the limit when a penalization parameter,
, tends to zero. The eigenvalues and eigenfunctions are determined either
analytically or numerically as functions of , both in the continuous case
and after applying Fourier or finite difference discretization schemes. For
fixed , we find that only the part of the spectrum corresponding to
eigenvalues approaches Dirichlet boundary
conditions, while the remainder of the spectrum is made of uncontrolled,
spurious wall modes. The penalization error for the controlled eigenfunctions
is estimated as a function of and . Surprisingly, in the Stokes
case, we show that the eigenfunctions approximately satisfy, with a precision
, Navier slip boundary conditions with slip length equal to
. Moreover, for a given discretization, we show that there exists
a value of , corresponding to a balance between penalization and
discretization errors, below which no further gain in precision is achieved.
These results shed light on the behavior of volume penalization schemes when
solving the Navier-Stokes equations, outline the limitations of the method, and
give indications on how to choose the penalization parameter in practical
cases
Aerodynamic ground effect in fruitfly sized insect takeoff
Aerodynamic ground effect in flapping-wing insect flight is of importance to
comparative morphologies and of interest to the micro-air-vehicle (MAV)
community. Recent studies, however, show apparently contradictory results of
either some significant extra lift or power savings, or zero ground effect.
Here we present a numerical study of fruitfly sized insect takeoff with a
specific focus on the significance of leg thrust and wing kinematics.
Flapping-wing takeoff is studied using numerical modelling and high performance
computing. The aerodynamic forces are calculated using a three-dimensional
Navier--Stokes solver based on a pseudo-spectral method with volume
penalization. It is coupled with a flight dynamics solver that accounts for the
body weight, inertia and the leg thrust, while only having two degrees of
freedom: the vertical and the longitudinal horizontal displacement. The natural
voluntary takeoff of a fruitfly is considered as reference. The parameters of
the model are then varied to explore possible effects of interaction between
the flapping-wing model and the ground plane. These modified takeoffs include
cases with decreased leg thrust parameter, and/or with periodic wing
kinematics, constant body pitch angle. The results show that the ground effect
during natural voluntary takeoff is negligible. In the modified takeoffs, when
the rate of climb is slow, the difference in the aerodynamic forces due to the
interaction with the ground is up to 6%. Surprisingly, depending on the
kinematics, the difference is either positive or negative, in contrast to the
intuition based on the helicopter theory, which suggests positive excess lift.
This effect is attributed to unsteady wing-wake interactions. A similar effect
is found during hovering
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