59 research outputs found
Information field dynamics for simulation scheme construction
Information field dynamics (IFD) is introduced here as a framework to derive
numerical schemes for the simulation of physical and other fields without
assuming a particular sub-grid structure as many schemes do. IFD constructs an
ensemble of non-parametric sub-grid field configurations from the combination
of the data in computer memory, representing constraints on possible field
configurations, and prior assumptions on the sub-grid field statistics. Each of
these field configurations can formally be evolved to a later moment since any
differential operator of the dynamics can act on fields living in continuous
space. However, these virtually evolved fields need again a representation by
data in computer memory. The maximum entropy principle of information theory
guides the construction of updated datasets via entropic matching, optimally
representing these field configurations at the later time. The field dynamics
thereby become represented by a finite set of evolution equations for the data
that can be solved numerically. The sub-grid dynamics is treated within an
auxiliary analytic consideration and the resulting scheme acts solely on the
data space. It should provide a more accurate description of the physical field
dynamics than simulation schemes constructed ad-hoc, due to the more rigorous
accounting of sub-grid physics and the space discretization process.
Assimilation of measurement data into an IFD simulation is conceptually
straightforward since measurement and simulation data can just be merged. The
IFD approach is illustrated using the example of a coarsely discretized
representation of a thermally excited classical Klein-Gordon field. This should
pave the way towards the construction of schemes for more complex systems like
turbulent hydrodynamics.Comment: 19 pages, 3 color figures, accepted by Phys. Rev.
Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET
In astrophysics, the two main methods traditionally in use for solving the
Euler equations of ideal fluid dynamics are smoothed particle hydrodynamics and
finite volume discretization on a stationary mesh. However, the goal to
efficiently make use of future exascale machines with their ever higher degree
of parallel concurrency motivates the search for more efficient and more
accurate techniques for computing hydrodynamics. Discontinuous Galerkin (DG)
methods represent a promising class of methods in this regard, as they can be
straightforwardly extended to arbitrarily high order while requiring only small
stencils. Especially for applications involving comparatively smooth problems,
higher-order approaches promise significant gains in computational speed for
reaching a desired target accuracy. Here, we introduce our new astrophysical DG
code TENET designed for applications in cosmology, and discuss our first
results for 3D simulations of subsonic turbulence. We show that our new DG
implementation provides accurate results for subsonic turbulence, at
considerably reduced computational cost compared with traditional finite volume
methods. In particular, we find that DG needs about 1.8 times fewer degrees of
freedom to achieve the same accuracy and at the same time is more than 1.5
times faster, confirming its substantial promise for astrophysical
applications.Comment: 21 pages, 7 figures, to appear in Proceedings of the SPPEXA
symposium, Lecture Notes in Computational Science and Engineering (LNCSE),
Springe
Modeling the Design Flow Coefficient of a Centrifugal Compressor Impeller
In calculating gas-dynamic characteristics by the universal modeling method it is necessary to determine a non-incidence flow rate through the blades of an impeller because of its relationship with the magnitude of incidence losses. The flow area decreased by the blades of finite thickness and the blades load have impact on the critical streamline direction. The universal modeling method in primary designing uses for this a scheme of replacing the influence of the blade load by the vortex effect with identical circulation. Finally, calculating the inviscid flow around the blades allows selecting a value of the inlet blade angle. For impellers with small design flow coefficients, the condition of the non-incidence inlet for the primary design and for the calculation of the inviscid flow is significantly different. The calculating correctness of the non-incidence regime for the non-viscous flow was checked earlier by measurements of the flow in the impellers. The paper presents CFD calculations of twenty impellers in a tenfold range of design flow coefficients. To provide correct comparison, it takes into account the differences in the value of the loading factor calculated by the programs of inviscid quasi-three-dimensional calculation and CFD programs. Shows the identity of inlet conditions for both methods. To increase primary design accuracy, the calculation model was refined. The formula for calculating vortex-induced velocity involves an empirical coefficient. The analysis of data for 32 impellers with different blade profiling allowed working out formulas for calculating empirical coefficient, depending on the type of an impeller, the blade load and the width of the throat at an impeller inlet. The new scheme-based calculation with the empirical coefficient is accurate enough for the primary design.</p
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