In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher t...In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.展开更多
We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation. These methods are discussed in the framework of the auxiliary space preconditioning method for ...We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation. These methods are discussed in the framework of the auxiliary space preconditioning method for generality. Unlike in the case of classical algebraic preconditioning methods, we take several analytical and physical considerations into account. In addition, we choose appropriate auxiliary problems to design the robust solvers herein. More importantly, our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators. We test the efficiency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems. The numerical results show that our methods are both efficient and robust for large reservoir models.展开更多
The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and res...The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.展开更多
Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski ga...Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpinski fractal as, for instance, a compact embedding result due to Fukushima and Shima.展开更多
Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t →＋∞,...Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t →＋∞, while if the coefficient matrix 19 of boundary conditions satisfies the boundary dissipative condition, the mixed initialboundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C1 solution, which also exponentially decays to zero as t →＋∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied.展开更多
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges Harbin Engineering University(Harbin)the National Natural Science Foundation of China+1 种基金Doctor Subject Foundation of the Ministry of Education of Chinathe"111"project(B07019)
文摘In this work, Green-Naghdi （GN） equations with general weight functions were derived in a simple way. A wave-absorbing beach was also considered in the general GN equations. A numerical solution for a level higher than 4 was not feasible in the past with the original GN equations. The GN equations for shallow water waves were simplified here, which make the application of high level （higher than 4） equations feasible. The linear dispersion relationships of the first seven levels were presented. The accuracy of dispersion relationships increased as the level increased. Level 7 GN equations are capable of simulating waves out to wave number times depth kd 〈 26. Numerical simulation of nonlinear water waves was performed by use of Level 5 and 7 GN equations, which will be presented in the next paper.
基金supported by Petro-China Joint Research Funding(Grant No.12HT1050002654)National Science Foundation of USA(Grant No.DMS-1217142)+1 种基金the Dean’s Startup FundAcademy of Mathematics and System Sciences and the State High Tech Development Plan of China(863 Program)(GrantNo.2012AA01A309)
文摘We study a class of preconditioners to solve large-scale linear systems arising from fully implicit reservoir simulation. These methods are discussed in the framework of the auxiliary space preconditioning method for generality. Unlike in the case of classical algebraic preconditioning methods, we take several analytical and physical considerations into account. In addition, we choose appropriate auxiliary problems to design the robust solvers herein. More importantly, our methods are user-friendly and general enough to be easily ported to existing petroleum reservoir simulators. We test the efficiency and robustness of the proposed method by applying them to a couple of benchmark problems and real-world reservoir problems. The numerical results show that our methods are both efficient and robust for large reservoir models.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872141, 11072168)the National Hi-Tech Research and Development Program of China ("863" Project) (Grant No. 2008AA042406)
文摘The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
基金supported by Grant CNCS PCE 47/2011 (Qualitative and Numerical Analysis of Nonlinear Problems on Fractals)supported by the GNAMPA Project(Esistenza e molteplicit di soluzioni per problemi differenziali non lineari) 2012
文摘Under an appropriate oscillating behavior either at zero or at infinity of the nonlinear data, the existence of a sequence of weak solutions for parametric quasilinear systems of the gradient-type on the Sierpinski gasket is proved. Moreover, by adopting the same hypotheses on the potential and in presence of suitable small perturbations, the same conclusion is achieved. The approach is based on variational methods and on certain analytic and geometrical properties of the Sierpinski fractal as, for instance, a compact embedding result due to Fukushima and Shima.
基金supported by the National Natural Science Foundation of China(Nos.11326159,11401421)the China Postdoctoral Science Foundation(No.2014M560287)the Shanxi Scholarship Council of China(No.2013-045)
文摘Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t →＋∞, while if the coefficient matrix 19 of boundary conditions satisfies the boundary dissipative condition, the mixed initialboundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C1 solution, which also exponentially decays to zero as t →＋∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied.
