Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-fron...Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.展开更多
In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also de...In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.展开更多
On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration ...On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.展开更多
基金Project(11272359)supported by the National Natural Science Foundation of China
文摘Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.
基金Supported by the National Natural Science Foundation of China under Grant Nos.71071013,71001004,and 71071012Foundation of Beijing Jiaotong University under Grant No.2009JBZ012-2
文摘In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model （COVM）, whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries （KdV） and modified KdV （mKdV） equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.
基金supported by the National Natural Science Foundation of China (Grant No. 51075208)the Innovation Project for Graduate Students of Jiangsu Province (Grant No. CX07B-162z)the Fund for Innovative and Excellent Doctoral Dissertation of NUAA (Grant No. BCXJ07-01)
文摘On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rota- tion and small strain established before and from the generalized-a time integration algorithm, the energy conserving and de- caying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserv- ing or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-a algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic respons- es of thin shells with large displacements and large rotations.
