A Novel Approach for Very High-order Transient Simulations with the Finite Volume Method – Recent Advances from the HIBforMBP Project
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In high-order finite-volume schemes, using a point-wise framework makes more easier for the local polynomial reconstruction and regularizes the order decay in arbitrary unstructured grids. Although, in unsteady cases the cell mean value is required to integrate, with high accuracy, the unsteady term of the governing equation. The accuracy of the point-wise based schemes is quantified for several grid types and steady problems. Additionally, it is shown that the stencil selection algorithm can have a significant impact in the computational efficiency, both in terms of memory and time costs. It is concluded that high-order time schemes can enhance the efficiencies of high-order spatial schemes. Furthermore, the point-wise framework is combined with immersed boundary method which reach eighth-order local accuracy, with an automatic p-adaptivity algorithm and finally its efficiency is evaluated with high-performance computing library PETSc. This talk summarizes the recent results from the HIBforMBP project.
