Kinetic scrape off layer simulations with semi-Lagrangian discontinuous Galerkin schemes

TL;DR

The paper introduces a GPU-friendly solver for scrape-off layer dynamics using a semi-Lagrangian discontinuous Galerkin method for the Vlasov–Poisson system, augmented by time-adaptive velocity space and a block-structured mesh to resolve sharp sheath gradients. A Strang time-splitting framework combines 1D advection solved by sLdG with a SIPG Poisson solve, enabling large time steps without CFL constraints. To suppress unphysical oscillations near the sheath while preserving efficiency on GPUs, the authors develop an in-step limiter with two indicator families and multiple modifiers, plus a computationally efficient limiter embedded in the advection step. The framework also includes adaptive velocity-domain truncation and spatial refinement near walls, and is validated via 1x1v SOL benchmarks demonstrating effective oscillation control, reduced memory transfer overhead, and favorable GPU performance.

Abstract

In this paper we propose a semi-Lagrangian discontinuous Galerkin solver for the simulation of the scrape off layer for an electron-ion plasma. We use a time adaptive velocity space to deal with fast particles leaving the computational domain, a block structured mesh to resolve the sharp gradient in the plasma sheath, and limiters to avoid oscillations in the density function. In particular, we propose a limiter that can be computed directly from the information used in the semi-Lagrangian discontinuous Galerkin advection step. This limiter is particularly efficient on graphic processing units (GPUs) and compares favorable with limiters from the literature. We provide numerical results for a set of benchmark problems and compare different limiting strategies.

Figures (7)

• Figure 1: Left: Projection applied in a region with a steep derivative. Right: Projection applied in a smooth region. The blue curves are the input polynomials ($u_l$ and $u_r$) and the red curves are the projections $u_p$. Here polynomials of degree $k=3$ are used.
• Figure 2: Particle flux at the right boundary \ref{['eq:flux']} with coarse velocity resolution (top), fine velocity resolution (second from top), and coarse resolution with the adaptive velocity adjustment algorithm (second from bottom). In addition, the bottom plot shows how the largest speed that can be found in the system decreases in time. In all simulations $1200$ degrees of freedom are used in the spatial direction.
• Figure 3: Electron flux for the blob initial data at the right boundary \ref{['eq:flux']} with 1200 degrees of freedom in the spatial direction, 600 degrees of freedom in the velocity direction, and using the adaptive velocity adjustment. The different limiters used are indicated in the legends of the plots.
• Figure 4: The electron particle density for the blob initial data at time $t=2000$ is shown for different limiters. Top left: reference solution, meanerr indicator and line WENO modifier, $2400 \times 1200$ degrees of freedom. Top right: minmod indicator and line WENO modifier, $1200 \times 600$ degrees of freedom. Bottom left: meanerr indicator and line WENO modifier, $1200 \times 600$ degrees of freedom. Bottom right: the newly proposed sLdG limiter, $1200 \times 600$ degrees of freedom. In all simulations the adaptive velocity adjustment is used.
• Figure 5: Electron particle flux for the blob initial data using different refinement ratios close to the wall. The meanerr indicator and the line WENO modifier are applied and the total (i.e. in all blocks) number of degrees of freedom is $1200 \times 600$. As a comparison a fine x-grid (with $6000 \times 600$ degrees of freedom) simulation with the same limiter is shown.

Theorems & Definitions (2)

• Remark 1
• Remark 2