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README.md

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FiniteDiffWENO5.jl is a Julia package that implements a finite difference fifth order Weighted Essentially Non-Oscillatory (WENO) method on regular grids for advection terms in partial differential equations for 1D, 2D, and 3D problems. The current implementation is based on the WENO-Z scheme from [Borges et al. (2008)](10.1016/j.jcp.2007.11.038).
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Currently, the package focuses on non-conservative form of the advection terms ($\mathbf{v} \cdot \nabla u$) on collocated grid, and conservative form ($\nabla \cdot \mathbf{v} u$) on staggered grid with the advection velocity located on the sides of the cells. The time integration is performed using a third-order Strong Stability Preserving Runge-Kutta (SSP-RK3) method.
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Currently, the package focuses on non-conservative form of the advection terms ($\mathbf{v} \cdot \nabla u$) on collocated grid, and conservative form ($\nabla \cdot$ ($\mathbf{v} u$)) on staggered grid with the advection velocity located on the sides of the cells. The time integration is performed using a third-order Strong Stability Preserving Runge-Kutta (SSP-RK3) method.
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The core of the package is written in pure Julia, focusing on performance using CPUs but GPU support is available using KernelAbstractions.jl and Chmy.jl via an extension.
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