1,302 research outputs found
Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries
Efficient transport algorithms are essential to the numerical resolution of
incompressible fluid flow problems. Semi-Lagrangian methods are widely used in
grid based methods to achieve this aim. The accuracy of the interpolation
strategy then determines the properties of the scheme. We introduce a simple
multi-stage procedure which can easily be used to increase the order of
accuracy of a code based on multi-linear interpolations. This approach is an
extension of a corrective algorithm introduced by Dupont \& Liu (2003, 2007).
This multi-stage procedure can be easily implemented in existing parallel codes
using a domain decomposition strategy, as the communications pattern is
identical to that of the multi-linear scheme. We show how a combination of a
forward and backward error correction can provide a third-order accurate
scheme, thus significantly reducing diffusive effects while retaining a
non-dispersive leading error term.Comment: 14 pages, 10 figure
Simulating Radiating and Magnetized Flows in Multi-Dimensions with ZEUS-MP
This paper describes ZEUS-MP, a multi-physics, massively parallel, message-
passing implementation of the ZEUS code. ZEUS-MP differs significantly from the
ZEUS-2D code, the ZEUS-3D code, and an early "version 1" of ZEUS-MP distributed
publicly in 1999. ZEUS-MP offers an MHD algorithm better suited for
multidimensional flows than the ZEUS-2D module by virtue of modifications to
the Method of Characteristics scheme first suggested by Hawley and Stone
(1995), and is shown to compare quite favorably to the TVD scheme described by
Ryu et. al (1998). ZEUS-MP is the first publicly-available ZEUS code to allow
the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic
simulations are enabled via an implicit flux-limited radiation diffusion (FLD)
module. The hydrodynamic, MHD, and FLD modules may be used in one, two, or
three space dimensions. Self gravity may be included either through the
assumption of a GM/r potential or a solution of Poisson's equation using one of
three linear solver packages (conjugate-gradient, multigrid, and FFT) provided
for that purpose. Point-mass potentials are also supported. Because ZEUS-MP is
designed for simulations on parallel computing platforms, considerable
attention is paid to the parallel performance characteristics of each module.
Strong-scaling tests involving pure hydrodynamics (with and without
self-gravity), MHD, and RHD are performed in which large problems (256^3 zones)
are distributed among as many as 1024 processors of an IBM SP3. Parallel
efficiency is a strong function of the amount of communication required between
processors in a given algorithm, but all modules are shown to scale well on up
to 1024 processors for the chosen fixed problem size.Comment: Accepted for publication in the ApJ Supplement. 42 pages with 29
inlined figures; uses emulateapj.sty. Discussions in sections 2 - 4 improved
per referee comments; several figures modified to illustrate grid resolution.
ZEUS-MP source code and documentation available from the Laboratory for
Computational Astrophysics at http://lca.ucsd.edu/codes/currentcodes/zeusmp2
Differential quadrature method for space-fractional diffusion equations on 2D irregular domains
In mathematical physics, the space-fractional diffusion equations are of
particular interest in the studies of physical phenomena modelled by L\'{e}vy
processes, which are sometimes called super-diffusion equations. In this
article, we develop the differential quadrature (DQ) methods for solving the 2D
space-fractional diffusion equations on irregular domains. The methods in
presence reduce the original equation into a set of ordinary differential
equations (ODEs) by introducing valid DQ formulations to fractional directional
derivatives based on the functional values at scattered nodal points on problem
domain. The required weighted coefficients are calculated by using radial basis
functions (RBFs) as trial functions, and the resultant ODEs are discretized by
the Crank-Nicolson scheme. The main advantages of our methods lie in their
flexibility and applicability to arbitrary domains. A series of illustrated
examples are finally provided to support these points.Comment: 25 pages, 25 figures, 7 table
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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