New Third-Order Finite Volume Unequal-Sized WENO Lagrangian Schemes for Solving Euler Equations

Yan Tan, Hui Lv and Jun Zhu ()
Additional contact information
Yan Tan: State Key Laboratory of Mechanics and Control for Aerospace Structures, Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), Ministry of Industry and Information Technology (MIIT), Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Hui Lv: State Key Laboratory of Mechanics and Control for Aerospace Structures, Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), Ministry of Industry and Information Technology (MIIT), Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Jun Zhu: State Key Laboratory of Mechanics and Control for Aerospace Structures, Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles (NUAA), Ministry of Industry and Information Technology (MIIT), Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Mathematics, 2023, vol. 11, issue 23, 1-21

Abstract: In this paper, new third-order finite volume unequal-sized weighted essentially non-oscillatory (US-WENO) Lagrangian schemes are designed to solve Euler equations in two and three dimensions. The spatial reconstruction procedures are implemented by using a convex combination of a quadratic polynomial with several linear polynomials specified on unequal-sized stencils, so the new US-WENO Lagrangian schemes can achieve the designed third-order accuracy and maintain an essentially non-oscillatory property near strong discontinuities in multi-dimensions. Unlike the traditional WENO reconstruction procedures specified on unstructured meshes, the linear weights of these new two-dimensional and three-dimensional US-WENO spatial reconstructions can be selected as any positive numbers as long as their summation equals one and they are not related to the local mesh topology or the location of quadrature points. Moreover, the linear weights do not have to be recalculated even if the grid moves with the fluid, avoiding the appearance of negative linear weights, thus improving computation efficiency and robustness in multi-dimensional Lagrangian numerical simulations. Finally, extensive benchmark numerical cases are employed to display the excellent capability of the presented US-WENO Lagrangian schemes.

Keywords: Lagrangian scheme; finite volume; US-WENO reconstruction; unequal-sized stencil; high-order accuracy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/23/4842/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/23/4842/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:23:p:4842-:d:1292532

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().