Convergence of Pseudospectral Method for Solving Navier-Stokes Equations

A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres

In this work, we describe, analyze, and implement a pseudospectral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. Our spectrally accurate numerical error analysis is based on the Gevrey regularity of the solutions of the Navier-Stokes equations on the sphere. The scheme is designed for convenient application of...

On Kato’s Method for Navier–stokes Equations

We investigate Kato’s method for parabolic equations with a quadratic non-linearity in an abstract form. We extract several properties known from linear systems theory which turn out to be the essential ingredients for the method. We give necessary and sufficient conditions for these conditions and provide new and more general proofs, based on real interpolation. In application to the Navier-St...

20. A Dual-Primal FETI Method for solving Stokes/Navier-Stokes Equations

Convergence acceleration of Runge-Kutta schemes for solving the Navier-Stokes equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fo...

Convergence of a Navier-stokes-poisson Approximation of the Incompressible Navier-stokes Equations

This paper studies the quasi-neutral limit of pressureless Navier-Stokes-Poisson equations in plasma physics in the torus T. For well prepared initial data the convergence of solutions of compressible Navier-Stokes-Poisson equations to the solutions of incompressible Navier-Stokes equations is justified rigorously by using the curl-div decomposition of the gradient. And a priori estimates with ...