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- W4313595462 abstract "This paper put forward a new fully discrete scheme construction method – double entropy condition solution formula method. With that, we turn the state-of-the-art semi-discrete WENO + RK scheme into a fully discrete scheme, which is named as Full-WENO. A major difficulty of this work is that we lack exact solution expressions for nonlinear equations in general cases. A feasible way we can go is to linearize equations and get quasi-exact solution formulas. The critical challenge is keeping both accuracy and efficiency in a scheme. Then, we get a class of new high-order schemes far better than traditional WENO schemes in the following aspects: (1) One-step to consistent high accuracy order in both space and time; (2) Resolution improves with the increasing CFL number; (3) Less CPU time and memory space, 1/s times of WENO with s-stage RK method in theory; (4) Excellent entropy condition satisfying property. Compared with our original work , the new method applies the more sophisticated WENO reconstruction and solves the resolution loss problems in multi-dimensional cases. The numerical tests show that the new scheme is equipped with the merits of high efficiency, high resolution and low dissipation, especially for long-time nonlinear problems." @default.
- W4313595462 created "2023-01-06" @default.
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- W4313595462 date "2023-01-06" @default.
- W4313595462 modified "2023-10-01" @default.
- W4313595462 title "Fully discrete WENO with double entropy condition for hyperbolic conservation laws" @default.
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- W4313595462 doi "https://doi.org/10.1080/19942060.2022.2145373" @default.
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