For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grid...For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.展开更多
In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference m...In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated.展开更多
Since governing equations are discretized using a finite volume method for FV TVD scheme, we use integral governing equations to solve the flow field. We achieve N S equations in terms of cylinder coordinate velocity ...Since governing equations are discretized using a finite volume method for FV TVD scheme, we use integral governing equations to solve the flow field. We achieve N S equations in terms of cylinder coordinate velocity components in an arbitrary curvilinear coordinate using a tensor analytic method to the integral governing equations. It’s also testified that term g which include Jacobian can be reduced when governing equations are discretized on an infinitesimal small control volume. Numerical calculations indicated that this scheme can capture shocks and contact discontinuities exactly and the solution with this treatment is in good agreement with the experimental data.展开更多
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced ...A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.展开更多
The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. T...The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.展开更多
An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adap...An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.展开更多
Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S)...Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.展开更多
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity u i and wave s...Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity u i and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.展开更多
We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently develo...We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.展开更多
文摘For a complex flow about multi-element airfoils a mixed grid method is set up. C-type grids are produced on each element′s body and in their wakes at first, O-type grids are given in the outmost area, and H-type grids are used in middle additional areas. An algebra method is used to produce the initial grids in each area. And the girds are optimized by elliptical differential equation method. Then C-O-H zonal patched grids around multi-element airfoils are produced automatically and efficiently. A time accurate finite-volume integration method is used to solve the compressible laminar and turbulent Navier-Stokes (N-S) equations on the grids. Computational results prove the method to be effective.
文摘In this paper, a numerical model is established. A modified N-S equation is used as a control equation for the wave field and porous flow area. The control equations are discreted and solved by the finite difference method. The free surface is tracked by the VOF method. The pressure field and velocity field of the whole flow area are solved by the reiterative iteration method. Finally, compared with the physical model test results of wave flume, the numerical model established in the present study is validated.
文摘Since governing equations are discretized using a finite volume method for FV TVD scheme, we use integral governing equations to solve the flow field. We achieve N S equations in terms of cylinder coordinate velocity components in an arbitrary curvilinear coordinate using a tensor analytic method to the integral governing equations. It’s also testified that term g which include Jacobian can be reduced when governing equations are discretized on an infinitesimal small control volume. Numerical calculations indicated that this scheme can capture shocks and contact discontinuities exactly and the solution with this treatment is in good agreement with the experimental data.
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
文摘A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.
文摘The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.
基金supported by the National Natural Science Foundation of China(11272152)
文摘An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.
文摘Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.
文摘Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity u i and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
基金supported by the NSF(No.DMS-1813071)(Chou)and the AFSOR(No.FA9550-22-1-0011)(Xiu).
文摘We present a numerical approach for modeling unknown dynamical systems using partially observed data,with a focus on biological systems with(relatively)complex dynamical behavior.As an extension of the recently developed deep neural network(DNN)learning methods,our approach is particularly suitable for practical situations when(i)measurement data are available for only a subset of the state variables,and(ii)the system parameters cannot be observed or measured at all.We demonstrate that,with a properly designed DNN structure with memory terms,effective DNN models can be learned from such partially observed data containing hidden parameters.The learned DNN model serves as an accurate predictive tool for system analysis.Through a few representative biological problems,we demonstrate that such DNN models can capture qualitative dynamical behavior changes in the system,such as bifurcations,even when the parameters controlling such behavior changes are completely unknown throughout not only the model learning process but also the system prediction process.The learned DNN model effectively creates a“closed”model involving only the observables when such a closed-form model does not exist mathematically.
