scholarly journals Sensitivities of Parcel Trajectories beneath the Lowest Scalar Model Level of a Lorenz Vertical Grid

2018 ◽  
Vol 146 (5) ◽  
pp. 1427-1435 ◽  
Author(s):  
Andrew Vande Guchte ◽  
Johannes M. L. Dahl

Abstract Parcel trajectory analysis has become commonplace in the study of simulated severe convection, particularly that which deals with the development and maintenance of near-ground vertical vorticity. However, there are a number of unsolved problems with analyzing simulated trajectories that exist near the ground. One of these unsolved problems is how to deal with parcels that pass beneath the lowest scalar model level. Using the CM1 model, which uses a Lorenz grid, the sensitivity of parcel characteristics such as location or potential temperature to the choice of common extrapolation methods is documented. Using potential temperature as an example, it is explained why unphysical tendencies of scalar variables along trajectories may arise once parcels descend beneath the lowest scalar model level. Given the poorly constrained flow (and scalar) fields beneath the lowest scalar model level, errors such as those documented here appear unavoidable when using free-slip boundary conditions.

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.


Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.


Sign in / Sign up

Export Citation Format

Share Document