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This study introduces a novel method to enhance numerical simulation accuracy for high-speed flows by refining the weighted essentially non-oscillatory (WENO) flux with higher-order corrections like the modified weighted compact scheme (MWCS). Numerical experiments demonstrate improved sharpness in capturing shock waves and stability in complex conditions like two interacting blast waves. Key highlights include simultaneous capture of small-scale smooth fluctuations and shock waves with precision surpassing the original WENO and MWCS methods. Despite the significantly improved accuracy, the extra computational cost brought by the new method is only marginally increased compared to the original WENO, and it outperforms MWCS in both accuracy and efficiency. Overall, this method enhances simulation fidelity and effectively balances accuracy and computational efficiency across various problems.
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Abstract Let 𝐺 be a finite solvable permutation group acting faithfully and primitively on a finite set Ω.Let G_{0}be the stabilizer of a point 𝛼 in Ω.The rank of 𝐺 is defined as the number of orbits of G_{0}in Ω, including the trivial orbit \{\alpha\}.In this paper, we completely classify the cases where 𝐺 has rank 5 and 6, continuing the previous works on classifying groups of rank 4 or lower.more » « less
