Higher-order finite-volume methods require special treatment near boundaries; that is the first topic in this lecture. Described are two approaches: using ghost cells on the outer side of solution domain boundary, and using adapted interpolation and differentiation methods in cells along boundaries.
The next topic is the implementation of Dirichlet and Neumann boundary condition in higher-order finite-volume methods.
The finite-volume methods described in Lectures 7 and 8 are then applied to one two-dimensional test case - the same one that was used for testing finite-difference methods in Lecture 6. Grid-dependence studies were performed with schemes of orders from 1st to 4th, on both uniform and non-uniform grids. In addition to the simple test code, commercial CFD software Simcenter STAR-CCM+ was also used with its default discretization methods, as used in industrial applications.
Finally, results obtained with finite-difference and finite-volume methods on grids with the same resolution are compared - with a surprising outcome.
You can download this video, the transcript of its soundtrack, the PowerPoint presentation file, and other supplementary material (computer codes for solving a 2D transport equation for a generic scalar, the same test case as used in Lecture 6 with finite-difference methods) from this site:
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You are also encouraged to participate in the discussion by posting comments, questions, and suggestions for improvements in the dedicated space for "The Perić Lectures on CFD" at the above site.