Aims of this paper are to improve ADI differential quadrature method （ADI-DQM） based on Bernstein polynomials and add a new application to the differential quadrature method. By using the new methodology, the numeri...Aims of this paper are to improve ADI differential quadrature method （ADI-DQM） based on Bernstein polynomials and add a new application to the differential quadrature method. By using the new methodology, the numerical solutions of the governing equations of unsteady two-dimensional flow of a polytropic gas are investigated. The numerical results reveal that the new technique is very effective and gives high accuracy, good convergence and reasonable stability.展开更多
An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood ...An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.展开更多
Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is...Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.展开更多
文摘Aims of this paper are to improve ADI differential quadrature method （ADI-DQM） based on Bernstein polynomials and add a new application to the differential quadrature method. By using the new methodology, the numerical solutions of the governing equations of unsteady two-dimensional flow of a polytropic gas are investigated. The numerical results reveal that the new technique is very effective and gives high accuracy, good convergence and reasonable stability.
基金the National Natural Science Foundation of China (No. 50778111)the Key Project of Fund of Science and Technology Development of Shanghai(No. 07JC14023)the Doctoral Disciplinary Special Research Project of Chinese Ministry of Education(No. 200802480056)
文摘An efficient iterative algorithm is presented for the numerical solution of viscous incompressible Navier-Stokes equations based on Taylor-Galerkin like split and pressure correction method in this paper. Taylor-Hood element is introduced to overcome the numerical difficulties arising from the fluid incompressibility. In order to confirm the properties of the algorithm, the numerical simulation on plane Poisseuille flow problem and lid- driven cavity flow problem with different Reynolds numbers is presented. The numerical results indicate that the proposed iterative version can be effectively applied to the simulation of viscous incompressible flows. Moreover, the proposed iterative version has a better overall performance in maximum time step size allowed, under comparable convergence rate, stability and accuracy, than other tested versions in numerical solutions of the plane PoisseuiUe flow with different Reynolds numbers ranging from low to high viscosities.
基金supported by the National Natural Science Foundation of China(Grant No.50876106)
文摘Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation–Pennes equation.The condition to decide temperature oscillation is obtained in this paper.In other cases the temperature would vary monotonously along geometric coordinates as time goes by.There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature.Besides its irreplaceable theoretical value,the analytical solution can also serve as standard solution to check numerical calculation,and therefore promote the development of numerical method of computational heat transfer.In addition,some new special methods have been given originally and deserved further attention.
