The project "High order structure-preserving semi-implicit schemes for hyperbolic equations" aimed at developing innovative numerical methods for compressible multi-phase and multi-material flows. A common aspect of all of them is that the governing PDE system usually takes the form of a hyperbolic balance law, with conservative nonlinear flux terms, non-conservative products and potentially stiff algebraic relaxation source terms. We considered models that are compatible with the first and second principle of thermodynamics, and which are endowed with involutions (stationary differential constraints) of the divergence and curl type which needs to be respected also at the discrete level.
The project has been coordinated by Prof. Michael Dumbser (Univ. Trento) and has been conducted by three research units (Trento, Sapienza and Insubria). Overall, this project has produced 31 journal papers (most of which have already been published) in leading international journals in the fields of numerical analysis, scientific computing and computational physics. The results have been presented on leading international conferences and two project workshops have been organized in order to maximize the visibility of the project, the first one in Como 23-24/01/2025 and the second one in Rome, 12-14/12/2025, see also https://sites.google.com/uniroma1.it/prin-closing-meeting/home.
In particular the research unit at Insubria has contributed by developing high order implicit timestepping methods (QUINPI) for finite volume discretizations of systems hyperbolic conservation laws in one and more space dimensions. In the same work package also novel time-limiting procedures have been explored. Additionally, the numerical entropy production error indicator has been extended to the ADER timestepping for finite volume schemes, and novel CWENOZ reconstructions suitable for boundary cells have been developed. Finally, a novel conservative semilagrangian approach, called SCOUT, have been proposed for advection-diffusion equations.
The project has been coordinated by Prof. Michael Dumbser (Univ. Trento) and has been conducted by three research units (Trento, Sapienza and Insubria). Overall, this project has produced 31 journal papers (most of which have already been published) in leading international journals in the fields of numerical analysis, scientific computing and computational physics. The results have been presented on leading international conferences and two project workshops have been organized in order to maximize the visibility of the project, the first one in Como 23-24/01/2025 and the second one in Rome, 12-14/12/2025, see also https://sites.google.com/uniroma1.it/prin-closing-meeting/home.
In particular the research unit at Insubria has contributed by developing high order implicit timestepping methods (QUINPI) for finite volume discretizations of systems hyperbolic conservation laws in one and more space dimensions. In the same work package also novel time-limiting procedures have been explored. Additionally, the numerical entropy production error indicator has been extended to the ADER timestepping for finite volume schemes, and novel CWENOZ reconstructions suitable for boundary cells have been developed. Finally, a novel conservative semilagrangian approach, called SCOUT, have been proposed for advection-diffusion equations.