ECOM: A fast and accurate solver for toroidal axisymmetric MHD equilibria

Lee, Jungpyo; Cerfon, Antoine

doi:10.1016/j.cpc.2015.01.015

Cited by 22 publications

(40 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where erf(·) is the error function, a and b are natural numbers, and the parameters H and s control the height and the steepness of the barrier respectively. The parameter ψ 0 gives the location of the transport barrier with respect to a common normalization where ψ ∈ [0, 1] [43,17]. In Figure 10 we present the behavior of the pressure as a function of ψ for different parameter values, and thus verify that we are able to model experimentally relevant situations [42, Figure 3].…”

Section: A Transport Barriermentioning

confidence: 58%

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Sánchez-Vizuet

Solano

Cerfon

2020

Computer Physics Communications

View full text Add to dashboard Cite

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

show abstract

Section: A Transport Barriermentioning

confidence: 58%

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Sánchez-Vizuet

Solano

Cerfon

2020

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

“…In section 2.3, we find the dependence of the Shafranov shift on the boundary tilt angle and show that the shift is insensitive to the shape of both the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). These analytic results are verified using equilibrium calculations performed with the numerical Grad-Shafranov solver ECOM [23]. Section 3 contains the results from nonlinear gyrokinetic simulations of the equilibria calculated in section 2.…”

mentioning

confidence: 74%

Effect of the Shafranov shift and the gradient ofβon intrinsic momentum transport in up–down asymmetric tokamaks

Ball

Parra

Lee

et al. 2016

Plasma Phys. Control. Fusion

Self Cite

View full text Add to dashboard Cite

Abstract.Tokamaks with up-down asymmetric poloidal cross-sections spontaneously rotate due to turbulent transport of momentum. In this work, we investigate the effect of the Shafranov shift on this intrinsic rotation, primarily by analyzing tokamaks with tilted elliptical flux surfaces. By expanding the Grad-Shafranov equation in the large aspect ratio limit we calculate the magnitude and direction of the Shafranov shift in tilted elliptical tokamaks. The results show that, while the Shafranov shift becomes up-down asymmetric and depends strongly on the tilt angle of the flux surfaces, it is insensitive to the shape of the current and pressure profiles (when the geometry, total plasma current, and average pressure gradient are kept fixed). Next, local nonlinear gyrokinetic simulations of these MHD equilibria are performed with GS2, which reveal that the Shafranov shift can significantly enhance the momentum transport. However, to be consistent, the effect of β (i.e. the radial gradient of β) on the magnetic equilibrium was also included, which was found to significantly reduce momentum transport. Including these two competing effects broadens the rotation profile, but leaves the on-axis value of the rotation roughly unchanged. Consequently, the shape of the β profile has a significant effect on the rotation profile of an up-down asymmetric tokamak.

show abstract

“…The adaptive refinement capability of our new solver plays a crucial role in guaranteeing an efficient use of the degrees of freedom in the system, and in obtaining high accuracy for the gradient of the potential. Finally, for the particular situations in which a smooth global extension is readily available without resorting to numerical computation, as is for example the case of an extension by zero in plasma physics applications [6], we have presented a numerical method which leads to the same order of convergence for the gradient of the potential as the potential itself. In our implementation of the FMM, this translates to 4th order convergence for both the potential and the gradient, and the order of convergence can be increased by choosing higher order basis functions [11].…”

Section: Resultsmentioning

confidence: 99%

An adaptive fast multipole accelerated Poisson solver for complex geometries

Askham

Cerfon

2017

Journal of Computational Physics

View full text Add to dashboard Cite

We present a fast, direct and adaptive Poisson solver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C 0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient "black box" fast solver.

show abstract

ECOM: A fast and accurate solver for toroidal axisymmetric MHD equilibria

Cited by 22 publications

References 74 publications

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

Effect of the Shafranov shift and the gradient ofβon intrinsic momentum transport in up–down asymmetric tokamaks

An adaptive fast multipole accelerated Poisson solver for complex geometries

Contact Info

Product

Resources

About