1,172 research outputs found
A Standard Test Case Suite for Two-Dimensional Linear Transport on the Sphere: Results from a Collection of State-of-the-Art Schemes
Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a minimal set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude–longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate–chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent.
The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data sets are made available to facilitate the process of model evaluation and scheme intercomparison
Coupled Vlasov and two-fluid codes on GPUs
We present a way to combine Vlasov and two-fluid codes for the simulation of
a collisionless plasma in large domains while keeping full information of the
velocity distribution in localized areas of interest. This is made possible by
solving the full Vlasov equation in one region while the remaining area is
treated by a 5-moment two-fluid code. In such a treatment, the main challenge
of coupling kinetic and fluid descriptions is the interchange of physically
correct boundary conditions between the different plasma models. In contrast to
other treatments, we do not rely on any specific form of the distribution
function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the
distribution function and a correction of the moments based on the fluid data.
Thus, throughout the simulation both codes provide the necessary boundary
conditions for each other. A speed-up factor of around 20 is achieved by using
GPUs for the computationally expensive solution of the Vlasov equation and an
overall factor of at least 60 using the coupling strategy combined with the GPU
computation. The coupled codes were then tested on the GEM reconnection
challenge
A Hybrid Godunov Method for Radiation Hydrodynamics
From a mathematical perspective, radiation hydrodynamics can be thought of as
a system of hyperbolic balance laws with dual multiscale behavior (multiscale
behavior associated with the hyperbolic wave speeds as well as multiscale
behavior associated with source term relaxation). With this outlook in mind,
this paper presents a hybrid Godunov method for one-dimensional radiation
hydrodynamics that is uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds
that the technique preserves certain asymptotic limits. The method incorporates
a backward Euler upwinding scheme for the radiation energy density and flux as
well as a modified Godunov scheme for the material density, momentum density,
and energy density. The backward Euler upwinding scheme is first-order accurate
and uses an implicit HLLE flux function to temporally advance the radiation
components according to the material flow scale. The modified Godunov scheme is
second-order accurate and directly couples stiff source term effects to the
hyperbolic structure of the system of balance laws. This Godunov technique is
composed of a predictor step that is based on Duhamel's principle and a
corrector step that is based on Picard iteration. The Godunov scheme is
explicit on the material flow scale but is unsplit and fully couples matter and
radiation without invoking a diffusion-type approximation for radiation
hydrodynamics. This technique derives from earlier work by Miniati & Colella
2007. Numerical tests demonstrate that the method is stable, robust, and
accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61
pages, 15 figures, 11 table
A standard test case suite for two-dimensional linear transport on the sphere
It is the purpose of this paper to propose a standard test case suite for two-dimensional transport schemes on the sphere intended to be used for model development and facilitating scheme intercomparison. The test cases are designed to assess important aspects of accuracy in geophysical fluid dynamics such as numerical order of convergence, "minimal" resolution, the ability of the transport scheme to preserve filaments, transport "rough" distributions, and to preserve pre-existing functional relations between species/tracers under challenging flow conditions. <br><br> The experiments are designed to be easy to set up. They are specified in terms of two analytical wind fields (one non-divergent and one divergent) and four analytical initial conditions (varying from smooth to discontinuous). Both conventional error norms as well as novel mixing and filament preservation diagnostics are used that are easy to implement. The experiments pose different challenges for the range of transport approaches from Lagrangian to Eulerian. The mixing and filament preservation diagnostics do not require an analytical/reference solution, which is in contrast to standard error norms where a "true" solution is needed. Results using the CSLAM (Conservative Semi-Lagrangian Multi-tracer) scheme on the cubed-sphere are presented for reference and illustrative purposes
- …