22,574 research outputs found
Problem-orientable numerical algorithm for modelling multi-dimensional radiative MHD flows in astrophysics -- the hierarchical solution scenario
We present a hierarchical approach for enhancing the robustness of numerical
solvers for modelling radiative MHD flows in multi-dimensions. This approach is
based on clustering the entries of the global Jacobian in a hierarchical manner
that enables employing a variety of solution procedures ranging from a purely
explicit time-stepping up to fully implicit schemes. A gradual coupling of the
radiative MHD equation with the radiative transfer equation in higher
dimensions is possible. Using this approach, it is possible to follow the
evolution of strongly time-dependent flows with low/high accuracies and with
efficiency comparable to explicit methods, as well as searching
quasi-stationary solutions for highly viscous flows. In particular, it is shown
that the hierarchical approach is capable of modelling the formation of jets in
active galactic nuclei and reproduce the corresponding spectral energy
distribution with a reasonable accuracy.Comment: 28 pages, 9 figure
Implementation of the LANS-alpha turbulence model in a primitive equation ocean model
This paper presents the first numerical implementation and tests of the
Lagrangian-averaged Navier-Stokes-alpha (LANS-alpha) turbulence model in a
primitive equation ocean model. The ocean model in which we work is the Los
Alamos Parallel Ocean Program (POP); we refer to POP and our implementation of
LANS-alpha as POP-alpha. Two versions of POP-alpha are presented: the full
POP-alpha algorithm is derived from the LANS-alpha primitive equations, but
requires a nested iteration that makes it too slow for practical simulations; a
reduced POP-alpha algorithm is proposed, which lacks the nested iteration and
is two to three times faster than the full algorithm. The reduced algorithm
does not follow from a formal derivation of the LANS-alpha model equations.
Despite this, simulations of the reduced algorithm are nearly identical to the
full algorithm, as judged by globally averaged temperature and kinetic energy,
and snapshots of temperature and velocity fields. Both POP-alpha algorithms can
run stably with longer timesteps than standard POP.
Comparison of implementations of full and reduced POP-alpha algorithms are
made within an idealized test problem that captures some aspects of the
Antarctic Circumpolar Current, a problem in which baroclinic instability is
prominent. Both POP-alpha algorithms produce statistics that resemble
higher-resolution simulations of standard POP.
A linear stability analysis shows that both the full and reduced POP-alpha
algorithms benefit from the way the LANS-alpha equations take into account the
effects of the small scales on the large. Both algorithms (1) are stable; (2)
make the Rossby Radius effectively larger; and (3) slow down Rossby and gravity
waves.Comment: Submitted to J. Computational Physics March 21, 200
Cardiac Electromechanics: The effect of contraction model on the mathematical problem and accuracy of the numerical scheme
Models of cardiac electromechanics usually contain a contraction model determining the active tension induced at the cellular level, and the equations of nonlinear elasticity to determine tissue deformation in response to this active tension. All contraction models are dependent on cardiac electro-physiology, but can also be dependent on\ud
the stretch and stretch-rate in the fibre direction. This fundamentally affects the mathematical problem being solved, through classification of the governing PDEs, which affects numerical schemes that can be used to solve the governing equations. We categorise contraction models into three types, and for each consider questions such as classification and the most appropriate choice from two numerical methods (the explicit and implicit schemes). In terms of mathematical classification, we consider the question of strong ellipticity of the total strain energy (important for precluding ‘unnatural’ material behaviour) for stretch-rate-independent contraction models; whereas for stretch-rate-dependent contraction models we introduce a corresponding third-order problem and explain how certain choices of boundary condition could lead to constraints on allowable initial condition. In terms of suitable numerical methods, we show that an explicit approach (where the contraction model is integrated in the timestep prior to the bulk deformation being computed) is: (i) appropriate for stretch-independent contraction models; (ii) only conditionally-stable, with the stability criterion independent of timestep, for contractions models which just depend on stretch (but not stretch-rate), and (iii) inappropriate for stretch-rate-dependent models
Towards a unified linear kinetic transport model with the trace ion module for EIRENE
Linear kinetic Monte Carlo particle transport models are frequently employed
in fusion plasma simulations to quantify atomic and surface effects on the main
plasma flow dynamics. Separate codes are used for transport of neutral
particles (incl. radiation) and charged particles (trace impurity ions).
Integration of both modules into main plasma fluid solvers provides then self
consistent solutions, in principle. The required interfaces are far from
trivial, because rapid atomic processes in particular in the edge region of
fusion plasmas require either smoothing and resampling, or frequent transfer of
particles from one into the other Monte Carlo code. We propose a different
scheme here, in which despite the inherently different mathematical form of
kinetic equations for ions and neutrals (e.g. Fokker-Planck vs. Boltzmann
collision integrals) both types of particle orbits can be integrated into one
single code. We show that the approximations and shortcomings of this "single
sourcing" concept (e.g., restriction to explicit ion drift orbit integration)
can be fully tolerable in a wide range of typical fusion edge plasma
conditions, and be overcompensated by the code-system simplicity, as well as by
inherently ensured consistency in geometry (one single numerical grid only) and
(the common) atomic and surface process modulesComment: 15 pages, 7 figure
Strong and auxiliary forms of the semi-Lagrangian method for incompressible flows
We present a review of the semi-Lagrangian method for advection-diusion and incompressible Navier-Stokes equations discretized with high-order methods. In particular, we compare the strong form where the departure points are computed directly via backwards integration with the auxiliary form where an auxiliary advection equation is solved instead; the latter is also referred to as Operator Integration Factor Splitting (OIFS) scheme. For intermediate size of time steps the auxiliary form is preferrable but for large time steps only the strong form is stable
Efficient Multigrid Preconditioners for Atmospheric Flow Simulations at High Aspect Ratio
Many problems in fluid modelling require the efficient solution of highly
anisotropic elliptic partial differential equations (PDEs) in "flat" domains.
For example, in numerical weather- and climate-prediction an elliptic PDE for
the pressure correction has to be solved at every time step in a thin spherical
shell representing the global atmosphere. This elliptic solve can be one of the
computationally most demanding components in semi-implicit semi-Lagrangian time
stepping methods which are very popular as they allow for larger model time
steps and better overall performance. With increasing model resolution,
algorithmically efficient and scalable algorithms are essential to run the code
under tight operational time constraints. We discuss the theory and practical
application of bespoke geometric multigrid preconditioners for equations of
this type. The algorithms deal with the strong anisotropy in the vertical
direction by using the tensor-product approach originally analysed by B\"{o}rm
and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend the
analysis to three dimensions under slightly weakened assumptions, and
numerically demonstrate its efficiency for the solution of the elliptic PDE for
the global pressure correction in atmospheric forecast models. For this we
compare the performance of different multigrid preconditioners on a
tensor-product grid with a semi-structured and quasi-uniform horizontal mesh
and a one dimensional vertical grid. The code is implemented in the Distributed
and Unified Numerics Environment (DUNE), which provides an easy-to-use and
scalable environment for algorithms operating on tensor-product grids. Parallel
scalability of our solvers on up to 20,480 cores is demonstrated on the HECToR
supercomputer.Comment: 22 pages, 6 Figures, 2 Table
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