Contributed Talk
A priori time limiting for the Quinpi scheme
University of Insubria, Italy
Abstract
The Quinpi numerical scheme proposed in [2,3] uses an implicit
third order Central Weighted Essentially Non-Oscillatory (CWENO) space reconstruction and
a third order Diagonally Implicit Runge⧿Kutta (DIRK3) scheme for the time integration.
In this work, we present a time limiting technique adopted from [1],
where an adaptive Runge-Kutta method is developed using a weighting procedure inspired
by spatial WENO methods. In our approach, we use this technique to modify the DIRK3 scheme.
Similarly to spatial WENO methods, a smoothness indicator is required.
Due to the predictor-corrector method used in the Quinpi scheme, we use the predicted values
of the solution for the smoothness indicator. We aim to solve hyperbolic systems of conservation laws,
especially the system of the Euler equations with a focus on the low-Mach number problems.
References
[1] Arbogast, T., Huang, Ch-S., Zhao, X., King, D. N.:
A third order, implicit, finite volume, adaptive Runge⧿Kutta WENO scheme for advection-diffusion equations,
Computer Methods in Applied Mechanics and Engineering, vol. 368, 2020.
[2] Puppo, G., Semplice, M., Visconti, G.:
Quinpi: Integrating conservation laws with CWENO implicit methods,
Communications on Applied Mathematics and Computation, vol. 5, 2023.
[3] Puppo, G., Visconti, G., Semplice, M.:
Quinpi: Integrating Stiff Hyperbolic Systems with Implicit High Order Finite Volume Schemes,
Communications in Computational Physics, vol. 36, 2024.
Joint work with Matteo Semplice.