A non-oscillatory finite volume scheme using a weighted smoothed reconstruction

• Published in: Journal of computational physics 2024-07, Vol.508, p.112981, Article 112981
• Main Authors: Mirzaei, Davoud, Soodbakhsh, Navid
• Format: Article
• Language: English
• Subjects: Conservation laws; Finite volume method; Polyharmonic splines; Radial basis functions; Weighted smoothed reconstruction (WSR)
• ISSN: 0021-9991; 1090-2716; 1090-2716
• DOI: 10.1016/j.jcp.2024.112981

In this research article, we introduce a high-order and non-oscillatory finite volume method in combination with radial basis function approximations and use it for the solution of scalar conservation laws on unstructured meshes. This novel approach departs from conventional non-oscillatory techniques, which often require the use of multiple stencils to achieve smooth reconstructions. Instead, the new method uses a single central stencil and hinges on an approximate interpolation methodology called the weighted smoothed reconstruction (WSR), with a foundation on polyharmonic spline interpolation. Through some numerical experiments, we demonstrate the efficiency and accuracy of the new approach. It reduces the computational cost and performs well in capturing shocks and sharp solution fronts. •Development of a novel reconstruction technique using RBFs for solving conservation laws in a FVM setting.•Applicable on unstructured meshes in different dimensions.•Overcoming some disadvantages of previous methods for stencil selection.•Being high-order and shock capturing, and applicable for problems with non-convex flux functions.•Observing average speedups of 2x compared to well-known available techniques.