We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.
The results of numerical analysis of turbine flow capacity and other parameters at different turbine rows are presented in this paper. Mass flow calculations by 3D Euler code has been controlled by means of 3D Navier-...The results of numerical analysis of turbine flow capacity and other parameters at different turbine rows are presented in this paper. Mass flow calculations by 3D Euler code has been controlled by means of 3D Navier-Stokes code taking into account inlet turbulence intensity and turbulence scale. The use of complicated numerical approaches (3D Euler or 3D Navier-Stokes codes) for mass flow definition demands close attention to quality of numerical techniques. Various reasons of inaccuracy of mass flow definition by using different 3D numerical approaches are analyzed.展开更多
In this manuscript, a proof for the age-old Riemann hypothesis is delivered, interpreting the Riemann Zeta function as an analytical signal, and using a signal analyzing affine model used in radar technology to match ...In this manuscript, a proof for the age-old Riemann hypothesis is delivered, interpreting the Riemann Zeta function as an analytical signal, and using a signal analyzing affine model used in radar technology to match the warped Riemann Zeta function on the time domain with its conjugate pair on the warped frequency domain (a Dirichlet series), through a scale invariant composite Mellin transform. As an application of above, since the Navier Stokes system solution’s Dirichlet transforms are also Dirichlet series, a minimal general solution of the 3d Navier Stokes differential equation for viscid incompressible flows is constructed through a fractional derivative Fourier transform of the found begin-solutions preserving the geometric properties of the 2d version assuming that the solution is an analytic solution that suffices the Laplace equation in cylindrical coordinates, which is the momentum equation for both the 2d and the 3d Navier Stokes systems of differential equations.展开更多
Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework...Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.展开更多
基金Acknowledgements Fan was supported by the National Natural Science Foundation of China （Grant No. 11171154） Li was supported by the National Natural Science Foundation of China （Grant Nos. 11271184, 11671193） and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘We prove two new regularity criteria for the 3D incompressible Navier-Stokes equations in a bounded domain. Our results also hold for the 3D Boussinesq system with zero heat conductivity.
文摘The results of numerical analysis of turbine flow capacity and other parameters at different turbine rows are presented in this paper. Mass flow calculations by 3D Euler code has been controlled by means of 3D Navier-Stokes code taking into account inlet turbulence intensity and turbulence scale. The use of complicated numerical approaches (3D Euler or 3D Navier-Stokes codes) for mass flow definition demands close attention to quality of numerical techniques. Various reasons of inaccuracy of mass flow definition by using different 3D numerical approaches are analyzed.
文摘In this manuscript, a proof for the age-old Riemann hypothesis is delivered, interpreting the Riemann Zeta function as an analytical signal, and using a signal analyzing affine model used in radar technology to match the warped Riemann Zeta function on the time domain with its conjugate pair on the warped frequency domain (a Dirichlet series), through a scale invariant composite Mellin transform. As an application of above, since the Navier Stokes system solution’s Dirichlet transforms are also Dirichlet series, a minimal general solution of the 3d Navier Stokes differential equation for viscid incompressible flows is constructed through a fractional derivative Fourier transform of the found begin-solutions preserving the geometric properties of the 2d version assuming that the solution is an analytic solution that suffices the Laplace equation in cylindrical coordinates, which is the momentum equation for both the 2d and the 3d Navier Stokes systems of differential equations.
基金the financial support by the National Natural Science Foundation of China (Grant No. 51490673)the Open Awards of the State Key Laboratory of Coastal and Offshore Engineering+1 种基金funded by the EPSRC MEMPHIS multiphase Programme (Grant No. EP/K003976/1)funding from the European Union Seventh Framework Programme (FP7/20072013) under grant agreement No. 603663 for the research project PEARL (Preparing for Extreme and Rare events in coasta L regions)
文摘Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.
