Skip to main content

LUP Student Papers

LUND UNIVERSITY LIBRARIES

An artificial viscosity approach for entropy stability

Tymoshchuk, Kateryna LU (2026) In Master’s Theses in Mathematical Sciences NUMM03 20261
Mathematics (Faculty of Engineering)
Mathematical Statistics
Mathematics (Faculty of Sciences)
Centre for Mathematical Sciences
Abstract
Numerical Weather Prediction (NWP) relies on the accurate and efficient numerical solution of nonlinear conservation laws governing atmospheric flows. However, high order DG methods are known to exhibit instabilities when applied to nonlinear conservation laws. Entropy stable methods improve the robustness of these schemes by imposing an entropy inequality on the solution and ensuring that the resulting numerical approximation is physically relevant and satisfies the laws of thermodynamics.

Previous work introduced an entropy stable method based on entropy correction artificial viscosity derived within the weak Discontinuous Galerkin (DG) formulation. The key idea is to add to the existing DG scheme an artificial viscosity term... (More)
Numerical Weather Prediction (NWP) relies on the accurate and efficient numerical solution of nonlinear conservation laws governing atmospheric flows. However, high order DG methods are known to exhibit instabilities when applied to nonlinear conservation laws. Entropy stable methods improve the robustness of these schemes by imposing an entropy inequality on the solution and ensuring that the resulting numerical approximation is physically relevant and satisfies the laws of thermodynamics.

Previous work introduced an entropy stable method based on entropy correction artificial viscosity derived within the weak Discontinuous Galerkin (DG) formulation. The key idea is to add to the existing DG scheme an artificial viscosity term designed to correct cell-wise violations of the entropy inequality. This thesis reformulates the scheme using the strong Direct Flux Reconstruction (DFR) form in order to apply it to a Numerical Weather Prediction model developed by Environment and Climate Change Canada (ECCC). The resulting scheme is implemented within Weather Factory codebase at ECCC. (Less)
Please use this url to cite or link to this publication:
author
Tymoshchuk, Kateryna LU
supervisor
organization
course
NUMM03 20261
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Numerical Weather Prediction, Euler Equations, High-Order Methods, Discontinuous Galerkin Method, Direct Flux Reconstruction, Entropy Stability, Artificial Viscosity
publication/series
Master’s Theses in Mathematical Sciences
report number
LUNFNA-3050-2026
ISSN
1404-6342
other publication id
2026:E80
language
English
id
9244553
date added to LUP
2026-07-27 11:01:24
date last changed
2026-07-27 11:01:24
@misc{9244553,
  abstract     = {{Numerical Weather Prediction (NWP) relies on the accurate and efficient numerical solution of nonlinear conservation laws governing atmospheric flows. However, high order DG methods are known to exhibit instabilities when applied to nonlinear conservation laws. Entropy stable methods improve the robustness of these schemes by imposing an entropy inequality on the solution and ensuring that the resulting numerical approximation is physically relevant and satisfies the laws of thermodynamics. 

Previous work introduced an entropy stable method based on entropy correction artificial viscosity derived within the weak Discontinuous Galerkin (DG) formulation. The key idea is to add to the existing DG scheme an artificial viscosity term designed to correct cell-wise violations of the entropy inequality. This thesis reformulates the scheme using the strong Direct Flux Reconstruction (DFR) form in order to apply it to a Numerical Weather Prediction model developed by Environment and Climate Change Canada (ECCC). The resulting scheme is implemented within Weather Factory codebase at ECCC.}},
  author       = {{Tymoshchuk, Kateryna}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master’s Theses in Mathematical Sciences}},
  title        = {{An artificial viscosity approach for entropy stability}},
  year         = {{2026}},
}