Communications in Mathematical Sciences

Volume 6 (2008)

Number 3

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

Pages: 569 – 593



Quang Huym Tran


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.


Linear advection, min-max principle, slope reconstruction, Arbitrary Lagrange- Euler (ALE) formalism

2010 Mathematics Subject Classification

35L65, 65M06, 76M12

Published 1 January 2008