A perfectly matched layer approach to the linearized shallow water equations models

Monthly Weather Review, 132 No.6, (2004), 1369 – 1378.A limited-area model of linearized shallow water equations (SWE) on an f-plane for a rectangular domain is considered. The rectangular domain is extended to include the so-called perfectly matched layer (PML) as an absorbing boundary condition. Following the proponent of the original method, the equations are obtained in this layer by splitting the shallow water equations in the coordinate directions and introducing the absorption coefficients. The performance of the PML as an absorbing boundary treatment is demonstrated using a commonly employed bell-shaped Gaussian initially introduced at the center of the rectangular physical domain

A perfectly matched layer formulation for the nonlinear shallow water equations models: The split equation approach

A limited-area model of nonlinear shallow water equations (SWE) with the Coriolis term in a rectangular domain is considered. The rectangular domain is extended to include the so-called perfectly matched layer (PML). Following the proponent of the original method, the PML equations are obtained by splitting the shallow water equations in the coordinate directions and introducing the damping terms. The efficacy of the PML boundary treatment is demonstrated in the case where a Gaussian pulse is initially introduced at the center of the rectangular physical domain. A systematic study is carried out for different mean convection speeds, and various values of the PML width and the damping coefficients. For the purpose of comparison, a reference solution is obtained on a fine grid on the extended domain with the characteristic boundary conditions. The L2 difference in the height field between the solution with the PML boundary treatment and the reference solution along a line at a downstream position in the interior domain is computed. The PML boundary treatment is found to yield better accuracy compared with both the characterisitic boundary conditions and the Engquist-Majda absorbing boundary conditions on an identical grid

Theoretical approaches to turbulence

xii; 373 hlm.: 21 Cm

Spectral Methods. Fundamentals in Single Domains

Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms. A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries

Una peculiar producción de cerámica de paredes finas en la Costa Catalana

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded

Upwind schemes, multigrid and defect correction for the steady Navier-Stokes equations

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