The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schem...The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.展开更多
In this paper, the accuracy of Chang＇s unstructured space-time conservation element and solution element （CE/SE） scheme is analysed for the first time. Based on a redefinition of conservation elements and solution ...In this paper, the accuracy of Chang＇s unstructured space-time conservation element and solution element （CE/SE） scheme is analysed for the first time. Based on a redefinition of conservation elements and solution elements, an improved two-dimensional （2D） unstructured CE/SE scheme with an adjustable parameter β is proposed to accurately capture shock waves. The new scheme can be applied to any type of grid without special treatnmnt. Compared with Chang＇s original parameter a, larger/5 dose not cost extra computational resources. Numerical tests reveal that the new scheme is not only clear in physical concept, compact and highly accurate but also more capable of capturing shock waves than the popular fifth-order accurate weighted essentially non-oscillatory scheme.展开更多
Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous how. Physi...Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous how. Physical guide lines are provided for the construction of these high order schemes. To avoid unduly ad hoc treatment in the boundary region the use of compact scheme is recommended because it has a small stencil size compared with the traditional finite difference scheme. Besides preliminary Fourier analysis shows the compact scheme can also yield better space resolution which makes it more suitable to study flow with multiscales e.g. turbulence. Other approaches such as perturbation method and finite spectral method are also emphasized. Typical numerical simulations were carried out. The first deals with Euler equations to show its capabilities to capture flow discontinuity. The second deals with Navier-Stokes Equations studying the evolution of a mixing layer, the pertinent structures at different times are shown. Asymmetric break down occurs and also the appearance of small vortices.展开更多
基金Project supported by the National Natural Science Foundation of China and the National Key Project for Basic Research.
文摘The coherent structure in two-dimensional mixing layers is simulated numerically with the compressible Navier-Stokes equations. The Navier-Stokes equations are discretized with high-order accurate upwind compact schemes. The process of development of flow structure is presented: loss of stability, development of Kelvin-Helmholtz instability, rolling up and pairing. The time and space development of the plane mixing layer and influence of the compressibility are investigated.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10732010 and 10972010)
文摘In this paper, the accuracy of Chang＇s unstructured space-time conservation element and solution element （CE/SE） scheme is analysed for the first time. Based on a redefinition of conservation elements and solution elements, an improved two-dimensional （2D） unstructured CE/SE scheme with an adjustable parameter β is proposed to accurately capture shock waves. The new scheme can be applied to any type of grid without special treatnmnt. Compared with Chang＇s original parameter a, larger/5 dose not cost extra computational resources. Numerical tests reveal that the new scheme is not only clear in physical concept, compact and highly accurate but also more capable of capturing shock waves than the popular fifth-order accurate weighted essentially non-oscillatory scheme.
基金The project supported by the National Natural Science Foundation of China(No.19393100)
文摘Numerical techniques play an important role in CFD. Some of them are reviewed in this paper. The necessity of using high order difference scheme is demonstrated for the study of high Reynolds number viscous how. Physical guide lines are provided for the construction of these high order schemes. To avoid unduly ad hoc treatment in the boundary region the use of compact scheme is recommended because it has a small stencil size compared with the traditional finite difference scheme. Besides preliminary Fourier analysis shows the compact scheme can also yield better space resolution which makes it more suitable to study flow with multiscales e.g. turbulence. Other approaches such as perturbation method and finite spectral method are also emphasized. Typical numerical simulations were carried out. The first deals with Euler equations to show its capabilities to capture flow discontinuity. The second deals with Navier-Stokes Equations studying the evolution of a mixing layer, the pertinent structures at different times are shown. Asymmetric break down occurs and also the appearance of small vortices.
