Periodic Reporting for period 1 - FASTKiT (Fully Adaptive Simulation Tool for Kinetic Theory)
Período documentado: 2020-04-01 hasta 2022-03-31
The increased dimensionality in velocity directions can be addressed by an extended set of fluid quantities via moment models or the maximum entropy method. To deal with the stiffness of the equations, asymptotic-preserving time discretization methods need to be used. Since both the stiffness and the accuracy of a kinetic model depend on space and time, the design of numerical methods incorporating fully integrated space-time adaptivity is crucial to allow these methods to be efficiently used in real-world applications.
In this action, the applicant will integrate his expertise on moment models with the experience on projective integration schemes available at the host institution, and extend their applicability towards a wide range of kinetic models hereby achieving the following objectives:
- Develop fully space-time adaptive numerical scheme for kinetic models
- Implement software for space-time adaptive solution of kinetic models
- Compute numerical solutions for real-world applications
The results of FASTKiT will constitute a major step forward in the adaptive simulation of kinetic models. FASTKiT will contribute to the development of technologies for next generation reactors and space exploration efforts, in line with Horizon 2020
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
Furthermore, the derivation of new moment models for free-surface flows has gained attention of the research community. Tailoring these models to applications in river and coastal engineering is expected to deliver benefits in the future.
We hope that our results of this project will contribute to the application of moment models in computational science and engineering to gain insights in complex physical processes.