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WENO-curvilinear

This repository encloses Mathematica codes used in the paper [1] on Fifth order finite volume Weighted essentially non-oscillatory scheme in orthogonally-curvilinear coordinates.

The two Mathematica codes are as follows:

  1. Weight derivation: For uniform grids in cartesian, cylindrical, and spherical coordinates
  2. Modified von-Neumann stability analysis (as performed in [3])

Figure 2: Rescaled spectrums (with maximum stable CFL number ~ σ) and stability domains of fifth−order WENO−C in spherical coordinates (m = 2) in a complex plane for different index numbers i=40

References:

  1. Shadab, M.A., Balsara, D., Shyy, W. and Xu, K., 2019. Fifth order finite volume WENO in general orthogonally-curvilinear coordinates. Computers & Fluids, 190, pp.398-424. Link
  2. Shadab, M.A., Ji, X. and Xu, K., 2020. Fifth-order finite-volume WENO on cylindrical grids. Spectral and High Order Methods for Partial Differential Equations, p.637. Link
  3. Liu, H. and Jiao, X., 2016. WLS-ENO: Weighted-least-squares based essentially non-oscillatory schemes for finite volume methods on unstructured meshes. Journal of Computational Physics, 314, pp.749-773. Link

Please cite paper [1,2], if using/extending the codes/work.