2,601 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 matrix stability analysis of the carbuncle phenomenon
The carbuncle phenomenon is a shock instability mechanism which ruins all efforts to compute grid-aligned shock
waves using low-dissipative upwind schemes. The present study develops a stability analysis for two-dimensional steady shocks on structured meshes based on the matrix method. The numerical resolution of the corresponding eigenvalue problem confirms the typical odd–even form of the unstable mode and displays a Mach number threshold effect currently observed in computations. Furthermore, the present method indicates that the instability of steady shocks is not only governed by the upstream Mach number but also by the numerical shock structure. Finally, the source of the instability is localized in the upstream region, providing some clues to better understand and control the onset of the carbuncle
Investigation of upwind, multigrid, multiblock numerical schemes for three dimensional flows. Volume 1: Runge-Kutta methods for a thin layer Navier-Stokes solver
A state-of-the-art computer code has been developed that incorporates a modified Runge-Kutta time integration scheme, upwind numerical techniques, multigrid acceleration, and multi-block capabilities (RUMM). A three-dimensional thin-layer formulation of the Navier-Stokes equations is employed. For turbulent flow cases, the Baldwin-Lomax algebraic turbulence model is used. Two different upwind techniques are available: van Leer's flux-vector splitting and Roe's flux-difference splitting. Full approximation multi-grid plus implicit residual and corrector smoothing were implemented to enhance the rate of convergence. Multi-block capabilities were developed to provide geometric flexibility. This feature allows the developed computer code to accommodate any grid topology or grid configuration with multiple topologies. The results shown in this dissertation were chosen to validate the computer code and display its geometric flexibility, which is provided by the multi-block structure
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
A Constrained Transport Scheme for MHD on Unstructured Static and Moving Meshes
Magnetic fields play an important role in many astrophysical systems and a
detailed understanding of their impact on the gas dynamics requires robust
numerical simulations. Here we present a new method to evolve the ideal
magnetohydrodynamic (MHD) equations on unstructured static and moving meshes
that preserves the magnetic field divergence-free constraint to machine
precision. The method overcomes the major problems of using a cleaning scheme
on the magnetic fields instead, which is non-conservative, not fully Galilean
invariant, does not eliminate divergence errors completely, and may produce
incorrect jumps across shocks. Our new method is a generalization of the
constrained transport (CT) algorithm used to enforce the condition on fixed Cartesian grids. Preserving at the discretized level is necessary to maintain the
orthogonality between the Lorentz force and . The possibility of
performing CT on a moving mesh provides several advantages over static mesh
methods due to the quasi-Lagrangian nature of the former (i.e., the mesh
generating points move with the flow), such as making the simulation
automatically adaptive and significantly reducing advection errors. Our method
preserves magnetic fields and fluid quantities in pure advection exactly.Comment: 13 pages, 9 figures, accepted to MNRAS. Animations available at
http://www.cfa.harvard.edu/~pmocz/research.htm
Deformable Overset Grid for Multibody Unsteady Flow Simulation
A deformable overset grid method is proposed to simulate the unsteady aerodynamic problems with multiple flexible moving bodies. This method uses an unstructured overset grid coupled with local mesh deformation to achieve both robustness and efficiency. The overset grid hierarchically organizes the subgrids into clusters and layers, allowing for overlapping/embedding of different type meshes, in which the mesh quality and resolution can be independently controlled. At each time step, mesh deformation is locally applied to the subgrids associated with deforming bodies by an improved Delaunay graph mapping method that uses a very coarse Delaunay mesh as the background graph. The graph is moved and deformed by the spring analogy method according to the specified motion, and then the computational meshes are relocated by a simple one-to-one mapping. An efficient implicit hole-cutting and intergrid boundary definition procedure is implemented fully automatically for both cell-centered and cell-vertex schemes based on the wall distance and an alternative digital tree data search algorithm. This method is successfully applied to several complex multibody unsteady aerodynamic simulations, and the results demonstrate the robustness and efficiency of the proposed method for complex unsteady flow problems, particularly for those involving simultaneous large relative motion and self-deformation
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