Second-order slope limiters for the simultaneous linear advection of (not so) independent variables

Abstract

Abstract. We propose a strategy to perform second-order enhancement using slope-limiters for the simultaneous linear advection of several scalar variables. Our strategy ensures a discrete min-max principle not only for each variable but also for any number of non-trivial combinations of them, which represent control variables. This problem arises in fluid mechanics codes using the Arbitrary Lagrange-Euler formalism, where the additional monotonicity property on control variables is required by physical considerations within the remap step.

Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian methods

“…In our terminology, this is a sequential method, that is, limiting of density gradient is not affected by bounds of other quantities. In the context of remapping, an interesting approach is introduced in [27]. It is also based on gradient limiting, but it is really a synchronous method.…”