University of Twente Student Theses
Bound-preserving limiting methods for Hybrid-DG discretization of linear advection equations
Kanger, B.J.D. (2024) Bound-preserving limiting methods for Hybrid-DG discretization of linear advection equations.
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| Abstract: | In many fields of physics, using numerical methods to solve systems described by partial differential equations play a crucial role. These solutions must follow certain laws of physics in order to have meaning. A solution u to a scalar conservation law is bounded when u_∗ ≤ u ≤ u^∗ for some global bounds u_∗ and u^∗. Yet, a numerical solution might violate these bounds. We can enforce these bounds for element averages by properly defining numerical fluxes between elements and limiting them. In this work, we formulate several methods for calculating numerical fluxes and how to limit them to ensure mass and bound preservation for HDG solutions. We extend the results of the work ”Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn–Hilliard equation”, by Florian Frank, Andreas Rupp and Dmitri Kuzmin (CMAME, 2020), by modifying their fractional step limiter procedure. We also define two separate slope limiters to ensure a pointwise bound preserved solution. This fractional step limiter (FSL) uses an implicit time scheme to calculate a higher and lower order solution, which is then used to calculate the limiting factors. |
| Item Type: | Essay (Bachelor) |
| Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |
| Subject: | 02 science and culture in general, 30 exact sciences in general, 31 mathematics, 33 physics, 54 computer science |
| Programme: | Applied Mathematics BSc (56965) |
| Link to this item: | https://purl.utwente.nl/essays/100727 |
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