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An efficient hybrid advection scheme in a level set framework coupling WENO5 and HOUC5 schemes based on kink detection

Abstract : We present a novel robust, accurate and efficient hybrid strategy by coupling WENO5 and HOUC5 schemes for the spatial discretization of the advection equation in a level set framework. This one is based on two main observations. First, from its definition, the level set function is globally a smooth function in the whole domain except where kink points are detected. And secondly, for smooth regions, the 5th order Weighted Essentially Non-Oscillatory (WENO5) scheme reduces to compute a 5th order High-Order Upstream Central (HOUC5) scheme, which has a lower computational cost. The introduced hybrid scheme HWH5, for hybrid WENO5 scheme HOUC5 scheme, coupled the robustness of a WENO5 scheme for all regions where the spatial discretization of the advection equation is subject to large error, i.e. where a kink is detected, with the efficiency of a HOUC5 scheme for smooth regions. The efficiency and robustness of this approach are demonstrated on a variety of benchmarks, where the hybrid approach presents equivalent results to the WENO5 scheme for a computational cost lowered with a factor up to 2. Alongside, we also present that the sole use of the efficient HOUC5 scheme for the spatial discretization of the advection equation presents anti-diffusive behaviors on the volume conservation and may lead to the introduction of noticeable perturbations of the interface which can be dreadful overtime on the overall dynamic. Conversely, WENO5 presents diffusive results in irregular regions. Hence, the adequate coupling of these two schemes in HWH5 allows obtaining a method as robust as WENO5 for a valuable lowered computational cost.
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https://hal.archives-ouvertes.fr/hal-03280902
Contributor : Félix Henri Connect in order to contact the contributor
Submitted on : Wednesday, July 7, 2021 - 4:56:32 PM
Last modification on : Friday, August 5, 2022 - 2:54:01 PM
Long-term archiving on: : Friday, October 8, 2021 - 6:54:59 PM

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  • HAL Id : hal-03280902, version 1

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Félix Henri, Mathieu Coquerelle, Pierre Lubin. An efficient hybrid advection scheme in a level set framework coupling WENO5 and HOUC5 schemes based on kink detection. {date}. ⟨hal-03280902⟩

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