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<p>To have proper multiscale simulations by central high-resolution schemes, the performance of slope limiters is crucial on adapted cells in terms of stability, accuracy, high-resolution, entropy-satisfying and spectral features. Hence, here, different families of slope limiters are extended or developed over non-uniform centered/non-centered cells, obtained by the wavelet-based adapted grids. The developed limiters on adaptive cells, are: (1) The entropy-satisfying limiter, (2) Second-order non-symmetric limited slopes and corresponding symmetric formulations, (3) Limiters with symmetric three-point stencils, second-order accuracy and the total variation diminishing (TVD) feature. The three-point stencil slope limiters do not preserve the symmetry feature on non-uniform cells. However, slopes obtained by non-symmetric stencils nearly preserve the symmetric property for different directions, as the direction-effect is inherent in their formulations. For non-symmetric limiters, firstly, corresponding TVD and monotonicity-preserving conditions are provided. Then, eight non-symmetric limited slopes are developed with four-, five- and three-point stencils. They are then unified to achieve four symmetric limiters. For the symmetric limiters with three-point stencils, also, the concept of blending of two limiters is updated to achieve compression-adaptive limiters. All limiters are used in the cell-adaptive Kurganov-Tadmor (KT) central scheme. Afterwards, the effects of limited slopes are studied on spectral properties. Finally, several problems are presented.</p>

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Multiscale Central High-Resolution Schemes with Different Types of Extended Slope Limiters on Wavelet-Based Adapted Cells

  • 期刊论文

  • 发表日期：

    2025年7月22日

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  • Hassan Yousefi,
  • Iradj Mahmoudzadeh Kani,
  • Timon Rabczuk

摘要

To have proper multiscale simulations by central high-resolution schemes, the performance of slope limiters is crucial on adapted cells in terms of stability, accuracy, high-resolution, entropy-satisfying and spectral features. Hence, here, different families of slope limiters are extended or developed over non-uniform centered/non-centered cells, obtained by the wavelet-based adapted grids. The developed limiters on adaptive cells, are: (1) The entropy-satisfying limiter, (2) Second-order non-symmetric limited slopes and corresponding symmetric formulations, (3) Limiters with symmetric three-point stencils, second-order accuracy and the total variation diminishing (TVD) feature. The three-point stencil slope limiters do not preserve the symmetry feature on non-uniform cells. However, slopes obtained by non-symmetric stencils nearly preserve the symmetric property for different directions, as the direction-effect is inherent in their formulations. For non-symmetric limiters, firstly, corresponding TVD and monotonicity-preserving conditions are provided. Then, eight non-symmetric limited slopes are developed with four-, five- and three-point stencils. They are then unified to achieve four symmetric limiters. For the symmetric limiters with three-point stencils, also, the concept of blending of two limiters is updated to achieve compression-adaptive limiters. All limiters are used in the cell-adaptive Kurganov-Tadmor (KT) central scheme. Afterwards, the effects of limited slopes are studied on spectral properties. Finally, several problems are presented.