Skip to content
DraconiticResearch
Search Sources API
197,787 studies31 sourcesUpdated 11 min ago
PreprintarXiv licencearXiv

Energy-conserving scheme for a shallow-water model with capillary effects

  • Sudarshan Kumar K
  • Boniface Nkonga
  • Praveen Chandrashekar
Open at sourcePDFDOICite

Abstract

We consider numerical approximations of shallow-water and thin-film flow models with capillary effects. These models lead to third-order differential equations, and we work with an augmented model with second-order derivatives. For a wide class of such models, which includes the classical shallow-water model and thin-film flow models, we develop a fully discrete energy-conserving scheme for both the quadratic and fully nonlinear capillary models. Numerical results show that the proposed scheme is stable and conserves total energy in the absence of dissipative effects.

Related

  1. Energy conserving compatible space--time FEM for deterministic and stochastic rotating shallow water
    Maneesh Kumar Singh, Colin J. Cotter
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. A Second-Order Semi-Implicit Projection Time-Stepping Scheme for the Shallow-Water Equations on the Sphere Using Compatible Finite Elements
    Karina Kowalczyk, Colin Cotter
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. A Discretely Entropy Conserving/Stable Flux Reconstruction Scheme via Hybridized Split Form Differential Operator and Generalized Entropy Projection
    Geng Liang, Junjie Wang, Hui Xu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingComputational physicsarXiv
  4. Explicit charge-conserving and modified energy-conserving PIC methods using the SAV approach
    Chengyu Fan, Nicolas Crouseilles, Jingwei Hu
    arXivPreprintCC BY 4.0Full textNumerical analysis & scientific computingarXiv
  5. Bottom-boundary identification using asymptotic observers in dispersive shallow-water models
    Vishal Neeraje, Vishal Vasan
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{kumar2026energyconserving,
  title = {{Energy-conserving scheme for a shallow-water model with capillary effects}},
  author = {Sudarshan Kumar K and Boniface Nkonga and Praveen Chandrashekar},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07360},
  eprint = {2611.07360},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07360},
}
RIS
TY  - UNPB
TI  - Energy-conserving scheme for a shallow-water model with capillary effects
AU  - Sudarshan Kumar K
AU  - Boniface Nkonga
AU  - Praveen Chandrashekar
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07360
UR  - https://arxiv.org/abs/2611.07360
AB  - We consider numerical approximations of shallow-water and thin-film flow models with capillary effects. These models lead to third-order differential equations, and we work with an augmented model with second-order derivatives. For a wide class of such models, which includes the classical shallow-water model and thin-film flow models, we develop a fully discrete energy-conserving scheme for both the quadratic and fully nonlinear capillary models. Numerical results show that the proposed scheme is stable and conserves total energy in the absence of dissipative effects.
ER  -