A high order positivity-preserving conservative WENO remapping method on 3D tetrahedral meshes

Lei, Nuo; Cheng, Juan; Shu, Chi‐Wang

doi:10.1016/j.cma.2022.115037

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Dumbser et al [28][29][30][31][32] developed a class of high-order Lagrangian one-step ADER-WENO finite volume schemes for hyperbolic systems on triangular and tetrahedral meshes, and achieved spatial accuracy mainly by using associated robust WENO reconstructions [33,34]. Meanwhile, the ALE method has also been greatly developed, such as is shown in [35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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

Tan,

Lv,

Zhu

2023

Mathematics

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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.

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