Contributed Talk
Semi-Implicit approaches: from stiff problems to dispersive effects and sediment evolution
University of Catania, Italy
Abstract
The development of efficient and robust numerical schemes for hyperbolic systems with multiscale features
remains a crucial challenge in computational mathematics. Over the years, we have investigated and designed
high-order semi-implicit schemes tailored for various classes of problems, including hyperbolic systems
with relaxation terms, sediment transport models, and dispersive wave equations.
For relaxation systems, we have formulated semi-implicit strategies that efficiently handle stiff source terms
while preserving the asymptotic properties of the system [1,2,3].
In sediment transport modeling, we have applied high-order semi-implicit schemes to Exner-type equations,
ensuring accurate coupling between hydrodynamic and morphodynamic evolution [4,5,6].
More recently, our focus has shifted to dispersive systems, where we have developed and analyzed semi-implicit
discretizations for hyperbolic approximations of Serre–Green–Naghdi-type equations, achieving stability
and accuracy in the presence of nonlocal and nonlinear effects [7].
References
[1] E. M. and S. Boscarino,
Semi-implicit-Type Order-Adaptive CAT2 Schemes for Systems of Balance Laws with Relaxed Source Term,
Communications on Applied Mathematics and Computation, 2024.
[2] R. Loubere, E. M., C. Pares-Madroñal, G. Russo,
CAT-MOOD Methods for Conservation Laws in One Space Dimension,
SEMA SIMAI Springer Series, 2024, 35.
[3] E. M., R. Loubere, C. Pares-Madroñal, G. Russo,
An almost fail-safe a-posteriori limited high-order CAT scheme,
Journal of Computational Physics, 2024, 498, 112650.
[4] E. M., S. Avgerinos, M.J. Castro-Diaz, G. Russo,
A semi-implicit finite volume method for the Exner model of sediment transport,
Journal of Computational Physics, 2024, 499, 112714.
[5] E. M., G. Russo,
Boundary effects on wave trains in the Exner model of sedimental transport,
Bollettino dell'Unione Matematica Italiana, 2024, 17(2).
[6] J. Garres, E. Fernandez-Nieto, E. M., G. Russo,
High-order-Exner... ,
In preparation, 2025.
[7] W. Boscheri, E. M., M. Ricchiuto,
Serre-Green-Naghdi-type IMEX... ,
In preparation, 2025.