In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's m...In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.展开更多
In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A clas...In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.展开更多
The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian flu...The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.展开更多
The first part of this study is focused on the numerical modelling and experimental investigation of transonic flow through a 2D model of the male rotor-housing gap in a dry screw compressor.Numerical simulations of t...The first part of this study is focused on the numerical modelling and experimental investigation of transonic flow through a 2D model of the male rotor-housing gap in a dry screw compressor.Numerical simulations of the clearance flow are performed with the help of the in-house compressible Navier-Stokes solver.Experimental measurements based on the Schlieren method in Toepler configuration are carried out.The objective of the second part of the study is to derive the analytical solution of gas microflow development in a gap between two parallel plates.The microflow is assumed to be laminar,incompressible and the velocity slip boundary conditions are considered at the walls.The constant velocity profile is prescribed at the inlet.For the mathematical description of the problem,the Oseen equation is used.The analytical results are compared with the numerical ones obtained using the developed incompressible Navier-Stokes solver including the slip flow boundary conditions.展开更多
文摘In this paper we give an overview of the present state of fast solvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method.It is shown that block preconditioners form an excellent approach for the solution,however if the grids are not to fine preconditioning with a Saddle point ILU matrix(SILU) may be an attractive alternative. The applicability of all methods to stabilized elements is investigated.In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.
基金supported by the National Natural Science Foundation of China (No.10771173)the Zheng Ge Ru Foundation,the Hong Kong RGC Earmarked Research (Nos.CUHK4028/04P,CUHK4040/06P,CUHK4042/08P)the RGC Central Allocation (No.CA05/06.SC01)
文摘In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.
基金Project supported by the National Science Foundation,the 111 Project from the Ministry of Education of China at Fudan University and the COFRS award from Florida State University
文摘The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated.All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions(specified velocity).These examples include a family of(nonlinear 3D) plane parallel flows,a family of(nonlinear) parallel pipe flows,as well as flows with uniform injection and suction at the boundary.We also identify a key ingredient in establishing the validity of the Prandtl type theory,i.e.,a spectral constraint on the approximate solution to the Navier-Stokes system constructed by combining the inviscid solution and the solution to the Prandtl type system.This is an additional difficulty besides the wellknown issue related to the well-posedness of the Prandtl type system.It seems that the main obstruction to the verification of the spectral constraint condition is the possible separation of boundary layers.A common theme of these examples is the inhibition of separation of boundary layers either via suppressing the velocity normal to the boundary or by injection and suction at the boundary so that the spectral constraint can be verified.A meta theorem is then presented which covers all the cases considered here.
基金supported by the grant GACR 101/08/0623 of the Czech Science Foundation and by the research project MSM4977751303 of the Ministry of Education,Youth and Sports of the Czech Republic
文摘The first part of this study is focused on the numerical modelling and experimental investigation of transonic flow through a 2D model of the male rotor-housing gap in a dry screw compressor.Numerical simulations of the clearance flow are performed with the help of the in-house compressible Navier-Stokes solver.Experimental measurements based on the Schlieren method in Toepler configuration are carried out.The objective of the second part of the study is to derive the analytical solution of gas microflow development in a gap between two parallel plates.The microflow is assumed to be laminar,incompressible and the velocity slip boundary conditions are considered at the walls.The constant velocity profile is prescribed at the inlet.For the mathematical description of the problem,the Oseen equation is used.The analytical results are compared with the numerical ones obtained using the developed incompressible Navier-Stokes solver including the slip flow boundary conditions.
