A hybrid HWENO-based method of lines transpose approach for Vlasov simulations

A new type hybrid Hermite weighted essentially non-oscillatory (HWENO) schemes in the implicit method of lines transpose (MOL^T) framework is designed for solving one-dimensional linear transport equations and further applied to the Vlasov-Poisson (VP) simulations via dimensional splitting. Compared with the WENO-based MOL^T method given in J. Comput. Phys. 2016, 327: 337-367, the new proposed hybrid HWENO-based MOL^T scheme has two advantages. The first is the HWENO schemes using the stencils narrower than those of the WENO schemes with the same order of accuracy. The second is that the schemes can adapt between the linear scheme and the HWENO scheme automatically. In summary, the hybrid HWENO scheme keeps the simplicity and robustness of the simple WENO scheme, while it has higher efficiency with less numerical errors in smooth regions and less computational costs as well. Benchmark examples are given to demonstrate the robustness and good performance of the proposed scheme.