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<p>Based on the trigonometric polynomial interpolation technique, two fifth-order trigonometric weighted compact nonlinear schemes (TWCNS-AO and TWCNS-ZM) are constructed to solve the Euler and Navier-Stokes equations. A quartic trigonometric polynomial and three quadratic trigonometric polynomials are constructed on a five-point stencil and three three-point sub-stencils, respectively, to obtain the unknown numerical fluxes at cell edges. To enhance the numerical stability, the WENO-AO-type nonlinear interpolation method of adaptive order and a modified WENO-Z-type nonlinear interpolation method with a new global smoothness indicator are adopted to establish the TWCNS-AO and TWCNS-ZM schemes, respectively. The modified WENO-Z-type interpolation can improve the convergence performance of the TWCNS-ZM scheme even in the presence of second-order critical points. The approximate dispersion relation (ADR) analysis indicates the spectral characteristics of the TWCNS-ZM and TWCNS-AO schemes are improved. Numerical results are presented to validate the performance of the designed schemes, such as the accuracy, resolution and shock-capturing ability.</p>

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High-order trigonometric WCNS schemes for compressible Euler and Navier-Stokes equations

  • 期刊论文

  • 发表日期：

    2026年2月13日

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  • Qinghong Tang,
  • Yanqun Jiang,
  • Huanhuan Yang,
  • Yixin Zhu

摘要

Based on the trigonometric polynomial interpolation technique, two fifth-order trigonometric weighted compact nonlinear schemes (TWCNS-AO and TWCNS-ZM) are constructed to solve the Euler and Navier-Stokes equations. A quartic trigonometric polynomial and three quadratic trigonometric polynomials are constructed on a five-point stencil and three three-point sub-stencils, respectively, to obtain the unknown numerical fluxes at cell edges. To enhance the numerical stability, the WENO-AO-type nonlinear interpolation method of adaptive order and a modified WENO-Z-type nonlinear interpolation method with a new global smoothness indicator are adopted to establish the TWCNS-AO and TWCNS-ZM schemes, respectively. The modified WENO-Z-type interpolation can improve the convergence performance of the TWCNS-ZM scheme even in the presence of second-order critical points. The approximate dispersion relation (ADR) analysis indicates the spectral characteristics of the TWCNS-ZM and TWCNS-AO schemes are improved. Numerical results are presented to validate the performance of the designed schemes, such as the accuracy, resolution and shock-capturing ability.