The present work illustrates how, given a direct discretization of the Inverse Problem of Vector Calculus whose solution is frequently required in the simulation of many continuum models like the Navier-Stokes equations, it is possible to recur to classical and modern tools of linear algebra like the Gauss Transforms (GT) and the Singular Value Decomposition (SVD) in order to obtain both computational models and a theoretical explanation to some adopted closures for the BC. It is also shown how the SVD and the GT can be considered an application of a finite dimensions Petrov-Galerkin approach and simple practical cases are presented to clarify the various items.
Singular Value Decomposition and Gauss Transforms in the Numerical Solution of Navier-Stokes Equations
F S Marra;
1997
Abstract
The present work illustrates how, given a direct discretization of the Inverse Problem of Vector Calculus whose solution is frequently required in the simulation of many continuum models like the Navier-Stokes equations, it is possible to recur to classical and modern tools of linear algebra like the Gauss Transforms (GT) and the Singular Value Decomposition (SVD) in order to obtain both computational models and a theoretical explanation to some adopted closures for the BC. It is also shown how the SVD and the GT can be considered an application of a finite dimensions Petrov-Galerkin approach and simple practical cases are presented to clarify the various items.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
