In the previous studies, the high-order gas-kinetic schemes (HGKS) have achieved successes for unsteady flows on three-dimensional unstructured meshes. In this paper, to accelerate the rate of convergence for steady flows, the implicit non-compact and compact HGKSs are developed. For non-compact scheme, the simple weighted essentially non-oscillatory (WENO) reconstruction is used to achieve the spatial accuracy, where the stencils for reconstruction contain two levels of neighboring cells. Incorporate with the nonlinear generalized minimal residual (GMRES) method, the implicit non-compact HGKS is developed. In order to improve the resolution and parallelism of non-compact HGKS, the implicit compact HGKS is developed with Hermite WENO (HWENO) reconstruction, in which the reconstruction stencils only contain one level of neighboring cells. The cell averaged conservative variable is also updated with GMRES method. Simultaneously, a simple strategy is used to update the cell averaged gradient by the time evolution of spatial-temporal coupled gas distribution function. To accelerate the computation, the implicit non-compact and compact HGKSs are implemented with the graphics processing unit (GPU) using compute unified device architecture (CUDA). A variety of numerical examples, from the subsonic to supersonic flows, are presented to validate the accuracy, robustness and efficiency of both inviscid and viscous flows.
翻译:在先前的研究中,针对三维非结构化网格的非紧致和紧致高阶气体动力学格式(HGKS)已经在非稳态流中取得了成功。为了加速稳态流的收敛速度,本文开发了隐式非紧致和紧致HGKS。对于非紧致格式,使用简单的加权本质无振荡(WENO)重构达到空间精度要求,其中重构模板包含两个层级的相邻单元。同时,结合非线性广义最小残差(GMRES)方法,开发了隐式非紧致HGKS。为了提高非紧致HGKS的分辨率和并行性,使用Hermite WENO(HWENO)重构开发了隐式紧致HGKS,其中重构模板只包含一个层级的相邻单元。通过空间-时间耦合气体分布函数的时间演化,采用简单的策略更新单元平均的梯度。同时,使用统一计算设备架构(CUDA)将隐式非紧致和紧致HGKS实现到图形处理器(GPU)上以加速计算。提供了各种非黏性和黏性流的数值范例以验证两种流模型在准确性、鲁棒性和有效性方面的性能。