尽管以二阶精度格式为基础的计算流体力学(CFD)方法和软件已经在航空航天飞行器设计中发挥了重要的作用,但是由于二阶精度格式的耗散和色散较大,对于湍流、分离等多尺度流动现象的模拟,现有成熟的CFD软件仍难以给出满意的结果,为此CFD...尽管以二阶精度格式为基础的计算流体力学(CFD)方法和软件已经在航空航天飞行器设计中发挥了重要的作用,但是由于二阶精度格式的耗散和色散较大,对于湍流、分离等多尺度流动现象的模拟,现有成熟的CFD软件仍难以给出满意的结果,为此CFD工作者发展了众多的高阶精度计算格式.如果以适应的计算网格来分类,一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法.由于非结构/混合网格具有良好的几何适应性,基于非结构/混合网格的高阶精度格式近年来备受关注.本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展,重点介绍了空间离散方法,主要包括k-Exact和ENO/WENO等有限体积方法,间断伽辽金(DG)有限元方法,有限谱体积(SV)和有限谱差分(SD)方法,以及近来发展的各种DG/FV混合算法和将各种方法统一在一个框架内的CPR(correction procedure via reconstruction)方法等.随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题,包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等.在综述过程中,介绍了各种方法的优势与不足,其间介绍了作者发展的基于"静动态混合重构"的DG/FV混合算法.最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.展开更多
High-order Discontinuous Galerkin(DG) methods have been receiving more and more attentions in the area of Computational Fluid Dynamics(CFD) because of their high-accuracy property. However, it is still a challenge to ...High-order Discontinuous Galerkin(DG) methods have been receiving more and more attentions in the area of Computational Fluid Dynamics(CFD) because of their high-accuracy property. However, it is still a challenge to obtain converged solution rapidly when solving the Reynolds Averaged Navier–Stokes(RANS) equations since the turbulence models significantly increase the nonlinearity of discretization system. The overall goal of this research is to develop an Artificial Neural Networks(ANNs) model with low complexity acting as an algebraic turbulence model to estimate the turbulence eddy viscosity for RANS. The ANN turbulence model is off-line trained using the training data generated by the widely used Spalart–Allmaras(SA) turbulence model before the Optimal Brain Surgeon(OBS) is employed to determine the relevancy of input features.Using the selected relevant features, a fully connected ANN model is constructed. The performance of the developed ANN model is numerically tested in the framework of DG for RANS, where the‘‘DG+ANN' method provides robust and steady convergence compared to the ‘‘DG+SA' method. The results demonstrate the promising potential to develop a general turbulence model based on artificial intelligence in the future given the training data covering a large rang of flow conditions.展开更多
In this paper, we present further development of the local discontinuous Galerkin （LDG） method designed in [21] and a new dissipative discontinuous Galerkin （DG） method for the HuntermSaxton equation. The numerica...In this paper, we present further development of the local discontinuous Galerkin （LDG） method designed in [21] and a new dissipative discontinuous Galerkin （DG） method for the HuntermSaxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].展开更多
文摘尽管以二阶精度格式为基础的计算流体力学(CFD)方法和软件已经在航空航天飞行器设计中发挥了重要的作用,但是由于二阶精度格式的耗散和色散较大,对于湍流、分离等多尺度流动现象的模拟,现有成熟的CFD软件仍难以给出满意的结果,为此CFD工作者发展了众多的高阶精度计算格式.如果以适应的计算网格来分类,一般可以分为基于结构网格的有限差分格式、基于非结构/混合网格的有限体积法和有限元方法,以及各种类型的混合方法.由于非结构/混合网格具有良好的几何适应性,基于非结构/混合网格的高阶精度格式近年来备受关注.本文综述了近年来基于非结构/混合网格的高阶精度格式研究进展,重点介绍了空间离散方法,主要包括k-Exact和ENO/WENO等有限体积方法,间断伽辽金(DG)有限元方法,有限谱体积(SV)和有限谱差分(SD)方法,以及近来发展的各种DG/FV混合算法和将各种方法统一在一个框架内的CPR(correction procedure via reconstruction)方法等.随后简要介绍了高阶精度格式应用于复杂外形流动数值模拟的一些需要关注的问题,包括曲边界的处理方法、间断侦测和限制器、各种加速收敛技术等.在综述过程中,介绍了各种方法的优势与不足,其间介绍了作者发展的基于"静动态混合重构"的DG/FV混合算法.最后展望了基于非结构/混合网格的高阶精度格式的未来发展趋势及应用前景.
基金co-supported by the Aeronautical Science Foundation of China (Nos. 20151452021and 20152752033)the National Natural Science Foundation of China (No. 61732006)
文摘High-order Discontinuous Galerkin(DG) methods have been receiving more and more attentions in the area of Computational Fluid Dynamics(CFD) because of their high-accuracy property. However, it is still a challenge to obtain converged solution rapidly when solving the Reynolds Averaged Navier–Stokes(RANS) equations since the turbulence models significantly increase the nonlinearity of discretization system. The overall goal of this research is to develop an Artificial Neural Networks(ANNs) model with low complexity acting as an algebraic turbulence model to estimate the turbulence eddy viscosity for RANS. The ANN turbulence model is off-line trained using the training data generated by the widely used Spalart–Allmaras(SA) turbulence model before the Optimal Brain Surgeon(OBS) is employed to determine the relevancy of input features.Using the selected relevant features, a fully connected ANN model is constructed. The performance of the developed ANN model is numerically tested in the framework of DG for RANS, where the‘‘DG+ANN' method provides robust and steady convergence compared to the ‘‘DG+SA' method. The results demonstrate the promising potential to develop a general turbulence model based on artificial intelligence in the future given the training data covering a large rang of flow conditions.
基金supported by NSFC grant 10601055FANEDD of CAS and SRF for ROCS SEM+1 种基金supported by NSF grant DMS-0809086ARO grant W911NF-08-1-0520
文摘In this paper, we present further development of the local discontinuous Galerkin （LDG） method designed in [21] and a new dissipative discontinuous Galerkin （DG） method for the HuntermSaxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21].
