A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence

Abstract

Abstract. While developing a new semi-Lagrangian solver, the gap between a linear Landau run in 1D×1D and a 5D gyrokinetic simulation in toroidal geometry is quite huge. Intermediate test cases are welcome for testing the code. A new fully two-dimensional conservative semi-Lagrangian (CSL) method is presented here and is validated on 2D polar geometries. We consider here as building block, a 2D guiding-center type equation on an annulus and apply it on two test cases. First, we revisit a 2D test case previously done with a PIC approach [18] and detail the boundary conditions. Second, we consider a 4D drift-kinetic slab simulation (see [10]). In both cases, the new method appears to be a good alternative to deal with this type of models since it improves the lack of mass conservation of the standard semi-Lagrangian (BSL) method.

Guiding center simulations on curvilinear grids

“…, N 2 and using the partition of unity of the B-splines. Now, for ε > 0 and having (11), we get QΦ ε h | √ g |dη = 0, which is coherent with (12). As (11) may not be true, we can enforce it, replacingf h byf h − λ, such that (11) is true forf h − λ, that is taking λ = Qf h | √ g |dη/ Q | √ g |dη.…”

“…Note that the expression of the mass and electric energy (which are conserved quantities in this model, up to specifying boundary conditions [12]) are respectively given by…”

“…[34], [14] for cartesian geometry, [29], [12], [18] for circular geometry and [19] for D-shaped geometry). A reference on such models and different variants (change of geometry, extension to 3D) is the work of M. Shoucri (see e.g.…”

“…A reference on such models and different variants (change of geometry, extension to 3D) is the work of M. Shoucri (see e.g. [31] and references in [12,14], in particular [32]). Such system can already describe some physics; as an example, it can be seen as a limit of a Vlasov-Poisson system (see e.g.…”

“…[6] and [9,13,20] for the numerics). As emphasized in [12], it is a building block for future drift kinetic simulations. Guiding center semi-Lagrangian simulations on curvilinear grids have already been performed in [8]; but there the mesh was only made oblique and the Poisson solver was solved on cartesian grid.…”