538 research outputs found
Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting
KEEN waves are nonlinear, non-stationary, self-organized asymptotic states in
Vlasov plasmas outside the scope or purview of linear theory constructs such as
electron plasma waves or ion acoustic waves. Nonlinear stationary mode theories
such as those leading to BGK modes also do not apply. The range in velocity
that is strongly perturbed by KEEN waves depends on the amplitude and duration
of the ponderomotive force used to drive them. Smaller amplitude drives create
highly localized structures attempting to coalesce into KEEN waves. These cases
have much more chaotic and intricate time histories than strongly driven ones.
The narrow range in which one must maintain adequate velocity resolution in the
weakly driven cases challenges xed grid numerical schemes. What is missing
there is the capability of resolving locally in velocity while maintaining a
coarse grid outside the highly perturbed region of phase space. We here report
on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative
non-uniform cubic splines in velocity that tackles this problem head on. An
additional feature of our approach is the use of a new high-order
time-splitting scheme which allows much longer simulations per computational e
ort. This is needed for low amplitude runs which take a long time to set up
KEEN waves, if they are able to do so at all. The new code's performance is
compared to uniform grid simulations and the advantages quanti ed. The birth
pains associated with KEEN waves which are weakly driven is captured in these
simulations. These techniques allow the e cient simulation of KEEN waves in
multiple dimensions which will be tackled next as well as generalizations to
Vlasov-Maxwell codes which are essential to understanding the impact of KEEN
waves in practice
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Numerous formulations of finite volume schemes for the Euler and
Navier-Stokes equations exist, but in the majority of cases they have been
developed for structured and stationary meshes. In many applications, more
flexible mesh geometries that can dynamically adjust to the problem at hand and
move with the flow in a (quasi) Lagrangian fashion would, however, be highly
desirable, as this can allow a significant reduction of advection errors and an
accurate realization of curved and moving boundary conditions. Here we describe
a novel formulation of viscous continuum hydrodynamics that solves the
equations of motion on a Voronoi mesh created by a set of mesh-generating
points. The points can move in an arbitrary manner, but the most natural motion
is that given by the fluid velocity itself, such that the mesh dynamically
adjusts to the flow. Owing to the mathematical properties of the Voronoi
tessellation, pathological mesh-twisting effects are avoided. Our
implementation considers the full Navier-Stokes equations and has been realized
in the AREPO code both in 2D and 3D. We propose a new approach to compute
accurate viscous fluxes for a dynamic Voronoi mesh, and use this to formulate a
finite volume solver of the Navier-Stokes equations. Through a number of test
problems, including circular Couette flow and flow past a cylindrical obstacle,
we show that our new scheme combines good accuracy with geometric flexibility,
and hence promises to be competitive with other highly refined Eulerian
methods. This will in particular allow astrophysical applications of the AREPO
code where physical viscosity is important, such as in the hot plasma in galaxy
clusters, or for viscous accretion disk models.Comment: 26 pages, 21 figures. Submitted to MNRA
Mono-Dispersed Droplet Delivery in a Refrigerated Wind Tunnel
An aircraft may experience inlight ice accretion and corresponding reductions in performance and control when the vehicle encounters clouds of super-cooled water droplets. In order to study anti-icing coatings, the EADS-IW Surface Engineering Group is building a refrigerated wind tunnel. Several variations of droplet delivery systems were explored to determine the most effective way to introduce mono-dispersed droplets into the wind tunnel. To investigate this flow, timeurate, unsteady viscous flow simulations were performed using the Loci/CHEM flow solver with a multi-scale hybrid RANS/LES turbulence model. A Lagrangian droplet model was employed to simulate the movement of water droplets in the wind tunnel. It was determined that the droplet delivery system required pressure relief to properly orient the flow inside the droplet delivery tube. Additionally, a streamlined drop tube cross-section was demonstrated to reduce turbulence in the wake and decrease the variability in droplet trajectories in the test section
GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods
We present two new Lagrangian methods for hydrodynamics, in a systematic
comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The
new methods are designed to simultaneously capture advantages of both
smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement
(AMR) schemes. They are based on a kernel discretization of the volume coupled
to a high-order matrix gradient estimator and a Riemann solver acting over the
volume 'overlap.' We implement and test a parallel, second-order version of the
method with self-gravity & cosmological integration, in the code GIZMO: this
maintains exact mass, energy and momentum conservation; exhibits superior
angular momentum conservation compared to all other methods we study; does not
require 'artificial diffusion' terms; and allows the fluid elements to move
with the flow so resolution is automatically adaptive. We consider a large
suite of test problems, and find that on all problems the new methods appear
competitive with moving-mesh schemes, with some advantages (particularly in
angular momentum conservation), at the cost of enhanced noise. The new methods
have many advantages vs. SPH: proper convergence, good capturing of
fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical
viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing.
Advantages vs. non-moving meshes include: automatic adaptivity, dramatically
reduced advection errors & numerical overmixing, velocity-independent errors,
accurate coupling to gravity, good angular momentum conservation and
elimination of 'grid alignment' effects. We can, for example, follow hundreds
of orbits of gaseous disks, while AMR and SPH methods break down in a few
orbits. However, fixed meshes minimize 'grid noise.' These differences are
important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code,
user's guide, test problem setups, and movies are available at
http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm
Numerical instabilities of spherical shallow water models considering small equivalent depths
This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Shallow water models are often adopted as an intermediate step in the development of
atmosphere and ocean models, though they are usually tested only with fluid depths
relevant to barotropic fluids. Here we investigate numerical instabilities emerging in
shallow water models considering small fluid depths, which are relevant for baroclinic
fluids. Different numerical instabilities of similar nature are investigated. The first one is
due to the adoption of the vector invariant form of the momentum equations, related to
what is known as the Hollingsworth instability. We provide examples of this instability
with finite volume and finite element schemes used in modern quasi-uniform spherical
grid based models. The second is related to an energy conserving form of discretization
of the Coriolis term in finite difference schemes on latitude-longitude global models.
Simple test cases with shallow fluid depths are proposed as a means of capturing and
predicting stability issues that can appear in three-dimensional models using only twodimensional
shallow-water codes.Peixoto acknowledges the Sao Paulo Research Foundation (FAPESP) under the grant number 2016/18445-7 and the National Science and Technology Development Council (CNPq) under grant number 441328/2014-8. Thuburn was funded by the Natural Environment Research Council under the “Gung Ho” project (grant NE/1021136/1). Bell was supported by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101)
A New Computational Fluid Dynamics Code I: Fyris Alpha
A new hydrodynamics code aimed at astrophysical applications has been
developed. The new code and algorithms are presented along with a comprehensive
suite of test problems in one, two, and three dimensions.
The new code is shown to be robust and accurate, equalling or improving upon
a set of comparison codes. Fyris Alpha will be made freely available to the
scientific community.Comment: 59 pages, 27 figures For associated code see
http://www.mso.anu.edu.au/fyri
Large Eddy Simulations in Astrophysics
In this review, the methodology of large eddy simulations (LES) is introduced
and applications in astrophysics are discussed. As theoretical framework, the
scale decomposition of the dynamical equations for neutral fluids by means of
spatial filtering is explained. For cosmological applications, the filtered
equations in comoving coordinates are also presented. To obtain a closed set of
equations that can be evolved in LES, several subgrid scale models for the
interactions between numerically resolved and unresolved scales are discussed,
in particular the subgrid scale turbulence energy equation model. It is then
shown how model coefficients can be calculated, either by dynamical procedures
or, a priori, from high-resolution data. For astrophysical applications,
adaptive mesh refinement is often indispensable. It is shown that the subgrid
scale turbulence energy model allows for a particularly elegant and physically
well motivated way of preserving momentum and energy conservation in AMR
simulations. Moreover, the notion of shear-improved models for inhomogeneous
and non-stationary turbulence is introduced. Finally, applications of LES to
turbulent combustion in thermonuclear supernovae, star formation and feedback
in galaxies, and cosmological structure formation are reviewed.Comment: 64 pages, 23 figures, submitted to Living Reviews in Computational
Astrophysic
- …