Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they a...Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.展开更多
In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is us...In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is used to solve the nonlinear problem.We introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter q.In the second step,we solve the Stokes equation for velocity and pressure.In the third step,we solve the Darcy equation for the piezometric head in the porous media domain.We use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s equation.The stability analysis,under some condition △t≤k0,k0>0,is given.The error estimates prove our method has an optimal convergence rates.Finally,some numerical results are presented to show the performance of our algorithm.展开更多
文摘Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.
文摘In this report,we give a viscosity splitting method for the Navier-Stokes/Darcy problem.In this method,the Navier-Stokes/Darcy equation is solved in three steps.In the first step,an explicit/implicit formulation is used to solve the nonlinear problem.We introduce an artificial diffusion term qDu in our scheme whose purpose is to enlarge the time stepping and enhance numerical stability,especially for small viscosity parameter n,by choosing suitable parameter q.In the second step,we solve the Stokes equation for velocity and pressure.In the third step,we solve the Darcy equation for the piezometric head in the porous media domain.We use the numerical solutions at last time level to give the interface condition to decouple the Navier-Stokes equation and the Darcy’s equation.The stability analysis,under some condition △t≤k0,k0>0,is given.The error estimates prove our method has an optimal convergence rates.Finally,some numerical results are presented to show the performance of our algorithm.
