In this presentation, we introduce a robustfifth orderfinite difference Hermite weighted essentially non-oscillatory (HWENO) scheme for compressible Euler equations following the HWENO with limiter (HWENO-L) scheme (J. Comput. Phys., 472:111676, 2023). The HWENO-L scheme reduced storage and increased efficiency by using restricted derivatives only for time discretizations, however, it cannot control spurious oscillations well when facing strong shocks since the derivatives are directly used in spatial discretizations without any restrictions. To address such an issue, our proposed HWENO scheme performsflux reconstructions in thefinite difference framework without using the derivative value of a target cell, which can result in a simpler and more robust scheme. The resulting scheme is simpler while still achievingfifth order accuracy, so is more efficient. Besides, numerically wefind it is very robust for some extreme problems even without positivity-preserving limiters. The proposed scheme also inherits advantages of previous HWENO schemes, including arbitrary positive linear weights in theflux reconstructions, compact reconstructed stencils, and high resolution. Extensive numerical tests are performed to demonstrate thefifth order accuracy, efficiency, robustness, and high resolution of the proposed HWENO scheme.

Speaker Biography:

Qiu Jianxian, Professor at the School of Mathematical Sciences, Xiamen University, and Editorial Board Member of the internationally renowned journal "J.Comp. Phys." (Computational Physics). Engaged in research on computational fluid dynamics and numerical solutions for differential equations, significant achievements have been made in the study and application of discontinuous Galerkin (DG) and weighted essentially oscillation free (WENO) numerical methods, with over 100 published papers. Hosted one project from the National Natural Science Foundation, one project supported by the Joint Fund, and one project supported by the National Key Research and Development Program. Participated in the EU Sixth Framework Special Research Project and was the only non EU member of the project team. Invited to give conference reports at international conferences multiple times. Received one second prize of the 2020 Ministry of Education Natural Science Award and one second prize of the 2021 Fujian Provincial Natural Science Award.