1) we have combined projective integration and kinetic (moment) models to successfully overcome the time step constraint of standard schemes, leading to a speedup of up to 200.
2) we developed a spatially adaptive projective integration scheme based on domain decomposition and showed that a stable integration of the stiff model is possible, leading to a speedup of more than 800.
3) we developed a fully space-time adaptive projective integration scheme using the notation of embedded Runge-Kutta schemes. This is expected to further reduce runtime for time accurate and steady-state simulations.
4) we derived new shallow water moment models allow to represent vertical variations of velocity and benefit from projective integration, leading to increased accuracy of numerical simulations. These showed that these models exhibit non-trivial steady-states and are stable in equilibrium. We successfully applied the models to sediment transport and used projective integration to reduce the runtime by a factor of 55.
Exploitation and dissemination:
The results listed above have been or will be communicated to the research community with the goal of exploitation in future research projects and applications.
1) published: Projective Integration Schemes for Hyperbolic Moment Equations, J. Koellermeier, G. Samaey, Kinet. Relat. Mod., 14(2), 353-387, 2021
2) submitted: Spatially Adaptive Projective Integration Schemes For Stiff Hyperbolic Balance Laws With Spectral Gaps, J. Koellermeier, G. Samaey, submitted
3) in preparation: Projective Integration Methods in the Runge-Kutta Framework and the Extension to Adaptivity in Time, J. Koellermeier, G. Samaey, in preparation
4) published: Shallow Water Moment models for bedload transport problems, J. Garres-Díaz, M. J. Castro, J. Koellermeier, T. Morales de Luna, Commun. in Comput. Phys., 30(3), 903-941, 2021;
Equilibrium Stability Analysis of Hyperbolic Shallow Water Moment equations, Q. Huang, J. Koellermeier, W.-A. Yong, Math. Method. Appl. Sci., 2022;
Recent developments in modeling free-surface flows with vertically-resolved velocity profiles using moments, J. Koellermeier, Proceedings of the 26th Congress of Differential Equations and Applications (CEDYA) and 16th Congress of Applied Mathematics (CMA) 2021, Institutional Repository of the Oviedo University, p.247-252 2021;
submitted: Steady States and Well-balanced Schemes for Shallow Water Moment Equations with Topography, J. Koellermeier, E. Pimentel-Garcia, submitted
