含新型间断探测器的混合WCNS格式在间断无粘可压流的应用

为了让高精度数值格式在含间断和小尺度涡等复杂结构的超声速无粘可压缩流动情况下,仍能鲁棒地捕捉激波并快速得到流场高保真的模拟结果,研究了以子模板导数组合为基础的光滑度量算法,构造了精度与鲁棒性兼顾的新型间断探测器,使间断识别对小尺度涡也具有高分辨率；研究了混合加权紧致非线性格式(weighted compact nonlinear scheme, WCNS)方法,对流场中的光滑与间断区域分别使用线性与非线性加权格式求解,从而克服单一非线性格式在光滑区分辨率难以达到设计精度的问题。数值实验表明,使用新型间断探测器的混合WCNS格式对一维、二维Euler方程模拟结果良好,并且相比于在全流场使用局部特征分解的原始WCNS方法有计算效率的提高。

Hybrid WCNS scheme with new discontinuity detector applied to discontinuous inviscid compressible flows

In order to enable high-precision accurate schemes to robustly capture shock waves and quickly obtain high fidelity simulation results of the flow field in supersonic inviscid compressible flow calculations, which usually contains complex structures such as discontinuities and small-scale vortices, a smoothness measurement algorithms based on combinations of sub-stencil derivatives were studied, and a new discontinuity detector was developed to balance accuracy and robustness, making troubled-cell recognition highly resolved for small-scale vortices. Hybrid WCNS(weighted compact nonlinear scheme) methods were studied, which could solve smooth and discontinuous regions in the flow field using linear and nonlinear weighting schemes respectively, to overcome the difficulty of a single nonlinear scheme in achieving design accuracy in smooth areas. Numerical results show that the hybrid WCNS scheme with new discontinuity detector performs well in simulating one-dimensional and two-dimensional Euler equations, and has higher computational efficiency compared to the original WCNS method that uses local characteristic decomposition in the entire flow field.