6,826 research outputs found
Kinetic Solvers with Adaptive Mesh in Phase Space
An Adaptive Mesh in Phase Space (AMPS) methodology has been developed for
solving multi-dimensional kinetic equations by the discrete velocity method. A
Cartesian mesh for both configuration (r) and velocity (v) spaces is produced
using a tree of trees data structure. The mesh in r-space is automatically
generated around embedded boundaries and dynamically adapted to local solution
properties. The mesh in v-space is created on-the-fly for each cell in r-space.
Mappings between neighboring v-space trees implemented for the advection
operator in configuration space. We have developed new algorithms for solving
the full Boltzmann and linear Boltzmann equations with AMPS. Several recent
innovations were used to calculate the discrete Boltzmann collision integral
with dynamically adaptive mesh in velocity space: importance sampling,
multi-point projection method, and the variance reduction method. We have
developed an efficient algorithm for calculating the linear Boltzmann collision
integral for elastic and inelastic collisions in a Lorentz gas. New AMPS
technique has been demonstrated for simulations of hypersonic rarefied gas
flows, ion and electron kinetics in weakly ionized plasma, radiation and light
particle transport through thin films, and electron streaming in
semiconductors. We have shown that AMPS allows minimizing the number of cells
in phase space to reduce computational cost and memory usage for solving
challenging kinetic problems
A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies
We present a moving control volume (CV) approach to computing hydrodynamic
forces and torques on complex geometries. The method requires surface and
volumetric integrals over a simple and regular Cartesian box that moves with an
arbitrary velocity to enclose the body at all times. The moving box is aligned
with Cartesian grid faces, which makes the integral evaluation straightforward
in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of
velocity and pressure at the fluid-structure interface are avoided and
far-field (smooth) velocity and pressure information is used. We re-visit the
approach to compute hydrodynamic forces and torques through force/torque
balance equation in a Lagrangian frame that some of us took in a prior work
(Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two
approaches for IB methods, thanks to the use of Peskin's delta functions. Both
approaches are able to suppress spurious force oscillations and are in
excellent agreement, as expected theoretically. Test cases ranging from Stokes
to high Reynolds number regimes are considered. We discuss regridding issues
for the moving CV method in an adaptive mesh refinement (AMR) context. The
proposed moving CV method is not limited to a specific IB method and can also
be used, for example, with embedded boundary methods
Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization
The distribution of forces on the surface of complex, deforming geometries is
an invaluable output of flow simulations. One particular example of such
geometries involves self-propelled swimmers. Surface forces can provide
significant information about the flow field sensed by the swimmers, and are
difficult to obtain experimentally. At the same time, simulations of flow
around complex, deforming shapes can be computationally prohibitive when
body-fitted grids are used. Alternatively, such simulations may employ
penalization techniques. Penalization methods rely on simple Cartesian grids to
discretize the governing equations, which are enhanced by a penalty term to
account for the boundary conditions. They have been shown to provide a robust
estimation of mean quantities, such as drag and propulsion velocity, but the
computation of surface force distribution remains a challenge. We present a
method for determining flow- induced forces on the surface of both rigid and
deforming bodies, in simulations using re-meshed vortex methods and Brinkman
penalization. The pressure field is recovered from the velocity by solving a
Poisson's equation using the Green's function approach, augmented with a fast
multipole expansion and a tree- code algorithm. The viscous forces are
determined by evaluating the strain-rate tensor on the surface of deforming
bodies, and on a 'lifted' surface in simulations involving rigid objects. We
present results for benchmark flows demonstrating that we can obtain an
accurate distribution of flow-induced surface-forces. The capabilities of our
method are demonstrated using simulations of self-propelled swimmers, where we
obtain the pressure and shear distribution on their deforming surfaces
Investigation of mixed element hybrid grid-based CFD methods for rotorcraft flow analysis
Accurate first-principles flow prediction is essential to the design and development of rotorcraft, and while current numerical analysis tools can, in theory, model the complete flow field, in practice the accuracy of these tools is limited by various inherent numerical deficiencies. An approach that combines the first-principles physical modeling capability of CFD schemes with the vortex preservation capabilities of Lagrangian vortex methods has been developed recently that controls the numerical diffusion of the rotor wake in a grid-based solver by employing a vorticity-velocity, rather than primitive variable, formulation. Coupling strategies, including variable exchange protocols are evaluated using several unstructured, structured, and Cartesian-grid Reynolds Averaged Navier-Stokes (RANS)/Euler CFD solvers. Results obtained with the hybrid grid-based solvers illustrate the capability of this hybrid method to resolve vortex-dominated flow fields with lower cell counts than pure RANS/Euler methods
Eulerian-Lagrangian method for simulation of cloud cavitation
We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation
in a compressible liquid. The method is designed to capture the strong,
volumetric oscillations of each bubble and the bubble-scattered acoustics. The
dynamics of the bubbly mixture is formulated using volume-averaged equations of
motion. The continuous phase is discretized on an Eulerian grid and integrated
using a high-order, finite-volume weighted essentially non-oscillatory (WENO)
scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles
at the sub-grid scale, each of whose radial evolution is tracked by solving the
Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid
as the void fraction by using a regularization (smearing) kernel. In the most
general case, where the bubble distribution is arbitrary, three-dimensional
Cartesian grids are used for spatial discretization. In order to reduce the
computational cost for problems possessing translational or rotational
homogeneities, we spatially average the governing equations along the direction
of symmetry and discretize the continuous phase on two-dimensional or
axi-symmetric grids, respectively. We specify a regularization kernel that maps
the three-dimensional distribution of bubbles onto the field of an averaged
two-dimensional or axi-symmetric void fraction. A closure is developed to model
the pressure fluctuations at the sub-grid scale as synthetic noise. For the
examples considered here, modeling the sub-grid pressure fluctuations as white
noise agrees a priori with computed distributions from three-dimensional
simulations, and suffices, a posteriori, to accurately reproduce the statistics
of the bubble dynamics. The numerical method and its verification are described
by considering test cases of the dynamics of a single bubble and cloud
cavitaiton induced by ultrasound fields.Comment: 28 pages, 16 figure
A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting
An explicit moving boundary method for the numerical solution of
time-dependent hyperbolic conservation laws on grids produced by the
intersection of complex geometries with a regular Cartesian grid is presented.
As it employs directional operator splitting, implementation of the scheme is
rather straightforward. Extending the method for static walls from Klein et
al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme
calculates fluxes needed for a conservative update of the near-wall cut-cells
as linear combinations of standard fluxes from a one-dimensional extended
stencil. Here the standard fluxes are those obtained without regard to the
small sub-cell problem, and the linear combination weights involve detailed
information regarding the cut-cell geometry. This linear combination of
standard fluxes stabilizes the updates such that the time-step yielding
marginal stability for arbitrarily small cut-cells is of the same order as that
for regular cells. Moreover, it renders the approach compatible with a wide
range of existing numerical flux-approximation methods. The scheme is extended
here to time dependent rigid boundaries by reformulating the linear combination
weights of the stabilizing flux stencil to account for the time dependence of
cut-cell volume and interface area fractions. The two-dimensional tests
discussed include advection in a channel oriented at an oblique angle to the
Cartesian computational mesh, cylinders with circular and triangular
cross-section passing through a stationary shock wave, a piston moving through
an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil
profile.Comment: 30 pages, 27 figures, 3 table
Towards accurate three-dimensional simulation of dense multi-phase flows using cylindrical coordinates
Most industrial scale fluidized-bed reactors are cylindrical, and the cylindrical coordinate system is a natural choice for their CFD simulation. There are, however, subtle complexities associated with this choice when using the Two-Fluid Model. The center of the grid forms a computational “boundary” and requires special treatment. Conventionally, a free slip no-normal flow condition has been used which does not predict the hydrodynamics accurately even when predicted parameters are in good agreement with measurement. Another difficulty is posed by the extremely small cells near the grid center, especially when simulating small scale experiments. The presence of these small cells raises concerns over the applicability of the Two-Fluid Model and is known to result in slow simulation convergence. These issues are addressed in the present study and appropriate solutions are proposed including the centerline treatment and the use of a non-uniform grid. Finally, the study compares the Cartesian grid with the cylindrical grid for application to fluidization. It is shown that simulating a cylindrical bed using the cylindrical grid is not only more accurate but also more computationally efficient. The analysis presented along with the proven computational efficiency of the cylindrical grid is especially significant considering that modeling commercial scale reactors, with multiple solid phases and chemical reactions, not only will require accurate description of the fluidization process but will also be exceedingly expensive in terms of computational cost.BP (Firm
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