Multi-relaxation time lattice Boltzmann method is employed to study the later stages of Rayleigh Taylor instabilities. A heavy fluid is placed over an immiscible lighter fluid in an unstable equilibrium. Various initi...Multi-relaxation time lattice Boltzmann method is employed to study the later stages of Rayleigh Taylor instabilities. A heavy fluid is placed over an immiscible lighter fluid in an unstable equilibrium. Various initial disturbances are used to initiate the flow. The D2Q9 lattice arrangement is employed on the computational domain. The density distribution function is determined for both fluids, and a coloring function is used to highlight the two fluids. Interactive forces and body forces are modelled by using the Shah and Chert model. Three different initial disturbances are studied, and their late stages are examined. The classic mushroom structure can be seen on all three cases. Distortions of the mushroom structures are seen due to the effects of the boundary and the influence of the initial disturbance.展开更多
By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summari...By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.展开更多
The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms...The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived.展开更多
文摘Multi-relaxation time lattice Boltzmann method is employed to study the later stages of Rayleigh Taylor instabilities. A heavy fluid is placed over an immiscible lighter fluid in an unstable equilibrium. Various initial disturbances are used to initiate the flow. The D2Q9 lattice arrangement is employed on the computational domain. The density distribution function is determined for both fluids, and a coloring function is used to highlight the two fluids. Interactive forces and body forces are modelled by using the Shah and Chert model. Three different initial disturbances are studied, and their late stages are examined. The classic mushroom structure can be seen on all three cases. Distortions of the mushroom structures are seen due to the effects of the boundary and the influence of the initial disturbance.
基金supported by the National Natural Science Foundation of China (Grant No. 51279057)the Major Program of National Natural Science Foundation of China (Grant Nos. 51190090 and 51190091)+1 种基金the Ph.D. Programs Foundation of Ministry of Education of China (Grant No.20120094120018)the Fundamental Research Funds for the Central Universities of China (Grant No. 2012B00214)
文摘By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.
文摘The authors modify a method of Olde Daalhuis and Temme for representing the remainder and coefficients in Airy-type expansions of integrals.By using a class of rational functions,they express these quantities in terms of Cauchy-type integrals;these expressions are natural generalizations of integral representations of the coe?cients and the remainders in the Taylor expansions of analytic functions.By using the new representation,a computable error bound for the remainder in the uniform asymptotic expansion of the modified Bessel function of purely imaginary order is derived.
