Communications in Mathematical Sciences
Volume 6 (2008)
Second-order slope limiters for the simultaneous linear advection of (not so) independent variables
Pages: 569 – 593
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