Claudia I. Garcia

A Global Semi-Implicit Semi-Lagrangian Shallow-Water Model on Locally Refined Grids

Abstract A variable-resolution global shallow-water model has been developed. The scheme makes use of a two-time-level semi-implicit semi-Lagrangian discretization, and the variable-resolution grid is composed of a basic global uniform coarser grid, employing successive local refinements to obtain high resolution over a region of interest. The algorithm on the locally refined grid is implemented in an efficient way with the help of a multigrid method, employed in the solution of the (nonlinear) elliptic equation resulting from the semi-implicit discretization. The model is very stable and attains high resolution over the area of interest at considerably lower costs than that of a global model with uniform high resolution. The results of comparisons are presented. The use of local refinement techniques is shown to be an effective way to obtain variable resolution in finite-difference global models.

A global finite-difference semi-Lagrangian model for the adiabatic primitive equations

We develop a global semi-implicit semi-Lagrangian model for the atmospheric adiabatic primitive equations discretized through finite-differences. The model formulation includes a new semi-Lagrangian treatment of the continuity equation and a spatially averaged Eulerian handling of the orography. These techniques contribute to the accuracy and efficiency of the scheme. The semi-Lagrangian discretization makes the integration method very stable; we can carry out integrations with time-steps which by far exceed the CFL time-step limitations of Eulerian schemes. We carry out several numerical experiments, showing that good accuracy is achieved even when we triple the time-steps. Our numerical experiments also demonstrate the computational efficiency of the method; we can run 10 days simulations at fine resolutions in a few hours on a personal computer.

On Power-Associative Nilalgebras of Dimension N and Nilindex N-1

Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n − 1 based on the condition that n − 4 ≤ dim 𝔄3 ≤ n − 3. This paper is a continuation of [10], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2].

On Jordan-Nilalgebras of Index 3

We study commutative algebras that satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a new bound of the index of nilpotency. We prove that every commutative nilalgebra of nilindex 3 generated by k elements over a field of characteristic ≠ 2, 3 is nilpotent of index less than or equal to k + 5.

A global semi-Lagrangian model for the adiabatic primitive equations on locally refined grids

We developed a global semi-implicit two-time-level semi-Lagrangian model for the atmospheric adiabatic primitive equations discretized through finite-differences, on locally refined grids. The principal aim of the technique is to have high resolution over a region of interest through successive grid refinements of a relatively coarse global uniform mesh, and in this way, to obtain accurate forecasts over this region at much lower computational costs. We tested the method through experiments with standard test cases for global atmospheric dynamical cores and also with real meteorological data. For a few days of integration, we obtained forecasts over the region of interest with similar accuracy to predictions computed on very fine globally uniform meshes, in a very efficient method. For longer periods, unresolved features outside the refined areas eventually reach the region of interest and affect the quality of the results. Our conclusion is that the use of locally refined meshes, combined with a stable semi-Lagrangian semi-implicit method, provides an effective way to compute accurate short range regional predictions.