| Citation: | XU Weizheng, KONG Xiangshao, ZHENG Cheng, et al. An improved method for third-order WENO-Z scheme[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(12): 2400-2405. doi: 10.13700/j.bh.1001-5965.2016.0863(in Chinese)
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High resolution shock capturing schemes are of great significance for numerical simulation of flow fields containing shock waves. WENO-Z3N1, WENO-Z3N2 and WENO-Z3N3 schemes were constructed through different global smoothness indicators based on the third-order WENO-Z scheme (WENO-Z3 scheme). Several classical examples such as sod problem, interacting blast wave and shock entropy wave interaction were simulated to investigate the computing performance of the three schemes (WENO-Z3N1, WENO-Z3N2, WENO-Z3N3). Precision of the three schemes was analyzed theoretically according to Taylor series expansion. It is concluded that theoretical precision of the three schemes at non-critical points plays the important role in the actual computing performance after discussion on the relationship between the theoretical precision and actual calculation accuracy. Double Mach reflection problem was conducted to further verify the reliability of the above conclusion. The research in the present paper gives an improved method for third-order WENO-Z scheme:global smoothness indicators should be reasonably constructed to make scheme satisfy the requirement of design precision at non-critical points in the smooth flow fields.
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