In this paper, we review some recent studies on compressible turbulence conducted by the authors＇ group, which include fundamental studies on compressible isotropic turbulence （CIT） and applied studies on developin...In this paper, we review some recent studies on compressible turbulence conducted by the authors＇ group, which include fundamental studies on compressible isotropic turbulence （CIT） and applied studies on developing a con- strained large eddy simulation （CLES） for wall-bounded turbulence. In the first part, we begin with a newly pro- posed hybrid compact-weighted essentially nonoscillatory （WENO） scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet-turbulence interac- tion, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and for- mulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.展开更多
Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and ...Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and their evolutions.However,like many other high-order shock capturing schemes,WENO schemes also suffer from the problem that it can not easily converge to a steady state solution if there is a strong shock wave.This is a long-standing difficulty for high-order shock capturing schemes.In recent years,this non-convergence problem has been studied extensively for WENO schemes.Numerical tests show that the key reason of the non-convergence to steady state is the slight post shock oscillations,which are at the small local truncation error level but prevent the residue to settle down to machine zero.Several strategies have been proposed to reduce these slight post shock oscillations,including the design of new smoothness indicators for the fifth-order WENO scheme,the development of a high-order weighted interpolation in the procedure of the local characteristic projection for WENO schemes of higher order of accuracy,and the design of a new type of WENO schemes.With these strategies,the convergence to steady states is improved significantly.Moreover,the strategies are applicable to other types of weighted schemes.In this paper,we give a brief review on the topic of convergence to steady state solutions for WENO schemes applied to Euler equations.展开更多
基金supported by the National Natural Science Foundation of China (Grants 11221061, 91130001, and 11302006)the National Science Foundation for Postdoctoral Scientists of China (Grants 2011M500194 and 2012M520109)
文摘In this paper, we review some recent studies on compressible turbulence conducted by the authors＇ group, which include fundamental studies on compressible isotropic turbulence （CIT） and applied studies on developing a con- strained large eddy simulation （CLES） for wall-bounded turbulence. In the first part, we begin with a newly pro- posed hybrid compact-weighted essentially nonoscillatory （WENO） scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet-turbulence interac- tion, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and for- mulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.
基金The work of the first author was supported by NSFC grant 11732016The research of the second author was supported by NSFC grant 11872210The research of the third author was supported by NSF grant DMS-1719410.
文摘Weighted essentially non-oscillatory(WENO)schemes are a class of high-order shock capturing schemes which have been designed and applied to solve many fluid dynamics problems to study the detailed flow structures and their evolutions.However,like many other high-order shock capturing schemes,WENO schemes also suffer from the problem that it can not easily converge to a steady state solution if there is a strong shock wave.This is a long-standing difficulty for high-order shock capturing schemes.In recent years,this non-convergence problem has been studied extensively for WENO schemes.Numerical tests show that the key reason of the non-convergence to steady state is the slight post shock oscillations,which are at the small local truncation error level but prevent the residue to settle down to machine zero.Several strategies have been proposed to reduce these slight post shock oscillations,including the design of new smoothness indicators for the fifth-order WENO scheme,the development of a high-order weighted interpolation in the procedure of the local characteristic projection for WENO schemes of higher order of accuracy,and the design of a new type of WENO schemes.With these strategies,the convergence to steady states is improved significantly.Moreover,the strategies are applicable to other types of weighted schemes.In this paper,we give a brief review on the topic of convergence to steady state solutions for WENO schemes applied to Euler equations.
