Section: New Results

Eulerian method for Vlasov equation

Recurrence phenomenon for finite element grid based Vlasov solver

Participants: Michel Mehrenberger, Laurent Navoret, Nhung Pham (IRMA)

In this work, we focus on one difficulty arising in the numerical simulation of the Vlasov-Poisson system: when using a regular grid-based solver with periodic boundary conditions, perturbations present at the initial time artificially reappear at a later time. For regular finite-element mesh in velocity, we show that this recurrence time is actually linked to the spectral accuracy of the velocity quadrature when computing the charge density. In particular, choosing trigonometric quadrature weights optimally defers in time the occurrence of the recurrence phenomenon. Numerical results using both the Semi-Lagrangian Discontinuous Galerkin and the Finite Element / Semi-Lagrangian methods have been carried out and confirm the analysis.

Numerical scheme for sheath equilibria

Participants: Mehdi Badsi (Nantes University), Michel Mehrenberger, Laurent Navoret

We are interested in developing a numerical method for capturing stationary sheaths that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Ampère model proposed in [18]. The main question addressed in this work is to know if classical numerical schemes can preserve stationary solutions with boundary conditions, since these solutions are not a priori conserved at the discrete level. In the context of high-order semi-Lagrangian method, due to their large stencil, interpolation near the boundary of the domain also requires a specific treatment. As expected, we numerically observe that the preservation of the equilibria is very sensitive to the prescribed boundary conditions and high order schemes are mandatory to maintain the preservation of the energy in large times.

Realistic geometry for Gysela

Participants: N. Bouzat, C. Bressan, V. Grandgirard, G. Latu, M. Mehrenberger

In magnetically confined plasmas used in Tokamak, turbulence is responsible for specific transport that limits the performance of this kind of reactors. Gyrokinetic simulations are able to capture ion and electron turbulence that give rise to heat losses, but also require state-of-the-art HPC techniques to handle computation costs. Such simulations are a major tool to establish good operating regime in Tokamak such as ITER, which is currently being built. Some of the key issues to address more realistic gyrokinetic simulations are: efficient and robust numerical schemes, accurate geometric description, good parallelization algorithms. The framework of this work is the Semi-Lagrangian setting for solving the gyrokinetic Vlasov equation and the Gysela code. In this paper, a new variant for the interpolation method is proposed that can handle the mesh singularity in the poloidal plane at r = 0 (polar system is used for the moment in Gysela). A non-uniform meshing of the poloidal plane is proposed instead of uniform one in order to save memory and computations. The interpolation method, the gyroaverage operator, and the Poisson solver are revised in order to cope with non-uniform meshes. A mapping that establishes a bijection from polar coordinates to more realistic plasma shape is used to improve realism. Convergence studies are provided to establish the validity and robustness of our new approach.

Parallel computing for kinetic solvers

Participants: Ksander Ejjaaouani, Olivier Aumage, Julien Bigot, Michel Mehrenberger

Existing programming models tend to tightly interleave algorithms and optimizations in HPC simulation codes. This requires scientists to become experts in both the simulated domain and the optimization process and makes the code difficult to maintain and port to new architectures. This paper proposes the InKS programming model that decouples these two concerns with distinct languages for each. The simulation algorithm is expressed in the InKS pia language with no concern for machine-specific optimizations. Optimizations are expressed using both a family of dedicated optimizations DSLs (InKS O) and plain C++. InKS O relies on the InKS pia source to assist developers with common optimizations while C++ is used for less common ones. Our evaluation demonstrates the soundness of the approach by using it on synthetic benchmarks and the Vlasov-Poisson equation. It shows that InKS offers separation of concerns at no performance cost.