2,322 research outputs found
Binarized-octree generation for Cartesian adaptive mesh refinement around immersed geometries
We revisit the generation of balanced octrees for adaptive mesh refinement (AMR) of Cartesian domains with immersed complex geometries. In a recent short note (Hasbestan and Senocak, 2017) [42], we showed that the data locality of the Z-order curve in a hashed linear-octree generation method may not be perfect because of potential collisions in the hash table. Building on that observation, we propose a binarized-octree generation method that complies with the Z-order curve exactly. Similar to a hashed linear-octree generation method, we use Morton encoding to index the nodes of an octree, but use a red-black tree in place of the hash table. Red-black tree is a special kind of a binary tree, which we use for insertion and deletion of elements during mesh adaptation. By strictly working with the bitwise representation of an octree, we remove computer hardware limitations on the depth of adaptation on a single processor. Additionally, we introduce a geometry encoding technique for rapidly tagging a solid geometry for mesh refinement. Our results for several geometries with different levels of adaptations show that the binarized-octree generation method outperforms the linear-octree generation method in terms of runtime performance at the expense of only a slight increase in memory usage. The current AMR capability, rebl-AMR, is available as open-source software
A simple multigrid scheme for solving the Poisson equation with arbitrary domain boundaries
We present a new multigrid scheme for solving the Poisson equation with
Dirichlet boundary conditions on a Cartesian grid with irregular domain
boundaries. This scheme was developed in the context of the Adaptive Mesh
Refinement (AMR) schemes based on a graded-octree data structure. The Poisson
equation is solved on a level-by-level basis, using a "one-way interface"
scheme in which boundary conditions are interpolated from the previous coarser
level solution. Such a scheme is particularly well suited for self-gravitating
astrophysical flows requiring an adaptive time stepping strategy. By
constructing a multigrid hierarchy covering the active cells of each AMR level,
we have designed a memory-efficient algorithm that can benefit fully from the
multigrid acceleration. We present a simple method for capturing the boundary
conditions across the multigrid hierarchy, based on a second-order accurate
reconstruction of the boundaries of the multigrid levels. In case of very
complex boundaries, small scale features become smaller than the discretization
cell size of coarse multigrid levels and convergence problems arise. We propose
a simple solution to address these issues. Using our scheme, the convergence
rate usually depends on the grid size for complex grids, but good linear
convergence is maintained. The proposed method was successfully implemented on
distributed memory architectures in the RAMSES code, for which we present and
discuss convergence and accuracy properties as well as timing performances.Comment: 33 pages, 15 figures, accepted for publication in Journal of
Computational Physic
Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods
Afivo is a framework for simulations with adaptive mesh refinement (AMR) on
quadtree (2D) and octree (3D) grids. The framework comes with a geometric
multigrid solver, shared-memory (OpenMP) parallelism and it supports output in
Silo and VTK file formats. Afivo can be used to efficiently simulate AMR
problems with up to about unknowns on desktops, workstations or single
compute nodes. For larger problems, existing distributed-memory frameworks are
better suited. The framework has no built-in functionality for specific physics
applications, so users have to implement their own numerical methods. The
included multigrid solver can be used to efficiently solve elliptic partial
differential equations such as Poisson's equation. Afivo's design was kept
simple, which in combination with the shared-memory parallelism facilitates
modification and experimentation with AMR algorithms. The framework was already
used to perform 3D simulations of streamer discharges, which required tens of
millions of cells
RADAMESH: Cosmological Radiative Transfer for Adaptive Mesh Refinement Simulations
We present a new three-dimensional radiative transfer (RT) code, RADAMESH,
based on a ray-tracing, photon-conserving and adaptive (in space and time)
scheme. RADAMESH uses a novel Monte Carlo approach to sample the radiation
field within the computational domain on a "cell-by-cell" basis. Thanks to this
algorithm, the computational efforts are now focused where actually needed,
i.e. within the Ionization-fronts (I-fronts). This results in an increased
accuracy level and, at the same time, a huge gain in computational speed with
respect to a "classical" Monte Carlo RT, especially when combined with an
Adaptive Mesh Refinement (AMR) scheme. Among several new features, RADAMESH is
able to adaptively refine the computational mesh in correspondence of the
I-fronts, allowing to fully resolve them within large, cosmological boxes. We
follow the propagation of ionizing radiation from an arbitrary number of
sources and from the recombination radiation produced by H and He. The chemical
state of six species (HI, HII, HeI, HeII, HeIII, e) and gas temperatures are
computed with a time-dependent, non-equilibrium chemistry solver. We present
several validating tests of the code, including the standard tests from the RT
Code Comparison Project and a new set of tests aimed at substantiating the new
characteristics of RADAMESH. Using our AMR scheme, we show that properly
resolving the I-front of a bright quasar during Reionization produces a large
increase of the predicted gas temperature within the whole HII region. Also, we
discuss how H and He recombination radiation is able to substantially change
the ionization state of both species (for the classical Stroemgren sphere test)
with respect to the widely used "on-the-spot" approximation.Comment: 19 pages, 24 figures; accepted for publication in MNRAS, version with
high-resolution figures is avalaible at
http://www.ast.cam.ac.uk/~cantal/Papers/CP10.pd
Multigrid elliptic equation solver with adaptive mesh refinement
In this paper we describe in detail the computational algorithm used by our
parallel multigrid elliptic equation solver with adaptive mesh refinement. Our
code uses truncation error estimates to adaptively refine the grid as part of
the solution process. The presentation includes a discussion of the orders of
accuracy that we use for prolongation and restriction operators to ensure
second order accurate results and to minimize computational work. Code tests
are presented that confirm the overall second order accuracy and demonstrate
the savings in computational resources provided by adaptive mesh refinement.Comment: 12 pages, 9 figures, Modified in response to reviewer suggestions,
added figure, added references. Accepted for publication in J. Comp. Phy
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
We review a scalable two- and three-dimensional computer code for
low-temperature plasma simulations in multi-material complex geometries. Our
approach is based on embedded boundary (EB) finite volume discretizations of
the minimal fluid-plasma model on adaptive Cartesian grids, extended to also
account for charging of insulating surfaces. We discuss the spatial and
temporal discretization methods, and show that the resulting overall method is
second order convergent, monotone, and conservative (for smooth solutions).
Weak scalability with parallel efficiencies over 70\% are demonstrated up to
8192 cores and more than one billion cells. We then demonstrate the use of
adaptive mesh refinement in multiple two- and three-dimensional simulation
examples at modest cores counts. The examples include two-dimensional
simulations of surface streamers along insulators with surface roughness; fully
three-dimensional simulations of filaments in experimentally realizable
pin-plane geometries, and three-dimensional simulations of positive plasma
discharges in multi-material complex geometries. The largest computational
example uses up to million mesh cells with billions of unknowns on
computing cores. Our use of computer-aided design (CAD) and constructive solid
geometry (CSG) combined with capabilities for parallel computing offers
possibilities for performing three-dimensional transient plasma-fluid
simulations, also in multi-material complex geometries at moderate pressures
and comparatively large scale.Comment: 40 pages, 21 figure
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