A High-Order Monotonicity-Preserving Scheme for Linear Scalar Advection on 3-D Irregular Meshes

Quang Huy Tran (1) , Bruno Scheurer (2)

1 IFPEN - IFP Energies nouvelles
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives

In [J. Comput. Phys. 175 (2002), 454-486], we proposed a new scheme for the linear nonconservative transport equation on 2-D irregular meshes. We now extend this scheme to the most general case, i.e., linear conservative transport equation over 3-D distorted meshes, the velocity fields of which may be a function of space and time. Since conservativity is now a major issue, we will thoroughly discuss about the trade-offs between accuracy, monotonicity and conservativity. The greatest advantage of this new scheme, which is compact in space and multilevel in time, lies in the fact that it does conserve mass, preserve monotonicity while ensuring high-order accuracy in smooth regions. Its effectiveness is illustrated by numerical tests.

Domaines: Analyse numérique [math.NA]

Quang Huy Tran, Bruno Scheurer. A High-Order Monotonicity-Preserving Scheme for Linear Scalar Advection on 3-D Irregular Meshes. 2018. ⟨hal-01901909⟩