Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Barnes, Michael; Abel, Ian; Dorland, W.; Görler, T.; Hammett, G. W.; Jenko, F.

doi:10.1063/1.3323082

Cited by 83 publications

(122 citation statements)

References 47 publications

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“…[57][58][59][60][61][62] As in neutral fluid DNS, both approaches initialize the simulation with some very small amplitude fluctuations, which first grow exponentially at the linear growth rate(s) of the instabilities being considered (the "linear" phase), and then saturate at a finite amplitude set by the balance of these linear drives and nonlinear couplings between different wavenumbers (the "saturated" phase). The statistics of various quantities (such as mean energy flux or fluctuation power) from this saturated phase are then used for transport modeling predictions, 63,64 as well as comparisons with other models and experiments in V&V studies. Implicit in this approach is the assumption that the saturated phase represents a "statistical steady-state" from which well-converged estimates of the quantities of interest can be made, and that the results are independent of the initial conditions.…”

Section: Basics Of Turbulence and Transport Modeling In Magneticmentioning

confidence: 99%

Validation metrics for turbulent plasma transport

Holland

2016

Physics of Plasmas

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Developing accurate models of plasma dynamics is essential for confident predictive modeling of current and future fusion devices. In modern computer science and engineering, formal verification and validation processes are used to assess model accuracy and establish confidence in the predictive capabilities of a given model. This paper provides an overview of the key guiding principles and best practices for the development of validation metrics, illustrated using examples from investigations of turbulent transport in magnetically confined plasmas. Particular emphasis is given to the importance of uncertainty quantification and its inclusion within the metrics, and the need for utilizing synthetic diagnostics to enable quantitatively meaningful comparisons between simulation and experiment. As a starting point, the structure of commonly used global transport model metrics and their limitations is reviewed. An alternate approach is then presented, which focuses upon comparisons of predicted local fluxes, fluctuations, and equilibrium gradients against observation. The utility of metrics based upon these comparisons is demonstrated by applying them to gyrokinetic predictions of turbulent transport in a variety of discharges performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], as part of a multi-year transport model validation activity.

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Section: Basics Of Turbulence and Transport Modeling In Magneticmentioning

confidence: 99%

Validation metrics for turbulent plasma transport

Holland

2016

Physics of Plasmas

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“…Thus, GyroLES is likely to enable large parameters scans of gyrokinetic turbulence which can be used, e.g., to efficiently couple turbulence and transport codes (see, e.g., Ref. 29 ).…”

Section: Discussionmentioning

confidence: 99%

“…(28) and (29). Since they are always positive, it is guaranteed that the model has a dissipative effect on the free energy.…”

Section: Dynamic Procedures For Gyrokineticsmentioning

confidence: 99%

Dynamic procedure for filtered gyrokinetic simulations

Morel¹,

Navarro²,

Albrecht-Marc³

et al. 2012

Physics of Plasmas

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Large Eddy Simulations (LES) of gyrokinetic plasma turbulence are investigated as interesting candidates to decrease the computational cost. A dynamic procedure is implemented in the GENE code, allowing for dynamic optimization of the free parameters of the LES models (setting the amplitudes of dissipative terms). Employing such LES methods, one recovers the free energy and heat flux spectra obtained from highly resolved Direct Numerical Simulations (DNS). Systematic comparisons are performed for different values of the temperature gradient and magnetic shear, parameters which are of prime importance in Ion Temperature Gradient (ITG) driven turbulence. Moreover, the degree of anisotropy of the problem, that can vary with parameters, can be adapted dynamically by the method that shows Gyrokinetic Large Eddy Simulation (GyroLES) to be a serious candidate to reduce numerical cost of gyrokinetic solvers. I. MOTIVATION AND CONTEXTIn the area of fluid turbulence, theories are usually based on the notion of an inertial range in which the energy cascades from larger scales to (somewhat) smaller scales mediated by the quadratic nonlinearity. The role of the smallest scales is then to dissipate energy in the so-called dissipative range. In numerical simulations, this picture has led to the development of Large Eddy Simulation (LES) techniques that are based on the idea that neglecting the small scales can be compensated by introducing a dissipative model for the eddy viscosity 1 .A Direct Numerical Simulation (DNS) is supposed to retain all the scales from the injection range down to the dissipative range. This requires an enormous numerical effort in the case of high Reynolds number flows. On the contrary, a LES coarsens the simulation grid and only retains the largest scales (which are problem-dependent), while the small scales (which are assumed to be universal) are replaced by a model. In Fourier space, such a coarsening can be seen as the action of a low-pass filter. Since the scale range is truncated, the dissipation scales can not be reached, and the modeling basically consists of the introduction of artificial dissipation mechanisms. From a more mathematical viewpoint, one notes that the filtering operation does not commute with the nonlinear term that transfers energy from largest to smallest scales, and the major problem of LES consists in finding a satisfying closure for representing the influence of the unresolved scales.Recent gyrokinetic studies have shown that Ion Temperature Gradient (ITG) driven turbulence exhibits a direct and local cascade of a nonlinear invariant, namely the free energy. 2 Such a cascade is analogous to the kinetic energy cascade in three dimensional NavierStokes turbulence. The important difference is that the a) pmorel@ulb.ac.be quadratic conserved quantity in fluid dynamics is the kinetic energy, while it is the free energy in gyrokinetics. The latter quantity is the sum of both the perturbed entropy and the electrostatic energy. Transfers between entropy and electrostatic energy ar...

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“…In many problems of interest, the distribution function f a is close to a Maxwell-Boltzmann distribution, in which case one often writes f a = f Ma + h a , where f Ma is the Maxwell-Boltzmann distribution and h a f Ma [9,3,28]. The collision operator C(f a , f b ) may then be linearized about f Ma [26,2,29].…”

Section: Introductionmentioning

confidence: 99%

A Spectral Transform Method for Singular Sturm--Liouville Problems with Applications to Energy Diffusion in Plasma Physics

Wilkening¹,

Cerfon²

2015

SIAM J. Appl. Math.

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Abstract. We develop a spectrally accurate numerical method to compute solutions of a model PDE used in plasma physics to describe diffusion in velocity space due to Fokker-Planck collisions. The solution is represented as a discrete and continuous superposition of normalizable and nonnormalizable eigenfunctions via the spectral transform associated with a singular Sturm-Liouville operator. We present a new algorithm for computing the spectral density function of the operator that uses Chebyshev polynomials to extrapolate the value of the Titchmarsh-Weyl m-function from the complex upper half-plane to the real axis. The eigenfunctions and density function are rescaled, and a new formula for the limiting value of the m-function is derived to avoid amplification of roundoff errors when the solution is reconstructed. The complexity of the algorithm is also analyzed, showing that the cost of computing the spectral density function at a point grows less rapidly than any fractional inverse power of the desired accuracy. A WKB analysis is used to prove that the spectral density function is real analytic. Using this new algorithm, we highlight key properties of the PDE and its solution that have strong implications on the optimal choice of discretization method in large-scale plasma physics computations. 1. Introduction. Partial differential equations involving singular Sturm-Liouville operators with continuous spectra arise frequently in computational physics. Common approaches to solving them include domain truncation, which often regularizes the operator and makes the spectrum discrete, or projection onto finite dimensional orthogonal polynomial or finite element subspaces, which also leads to discrete spectra. Here we develop an alternative approach in which the continuous spectrum is treated analytically via a spectral transform, and the numerical challenge is in accurately representing and evaluating the integrals giving the exact solution.While the methods developed in this paper to diagonalize singular Sturm-Liouville operators are quite general, we will describe them in the context of velocity-space diffusion in one dimension,

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Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Cited by 83 publications

References 47 publications

Validation metrics for turbulent plasma transport

Validation metrics for turbulent plasma transport

Dynamic procedure for filtered gyrokinetic simulations

A Spectral Transform Method for Singular Sturm--Liouville Problems with Applications to Energy Diffusion in Plasma Physics

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