Paper Info
Title
A Semi-Lagrangian Numerical Method for the Three-Dimensional Advection Problem with an Isoparametric Transformation of Subdomains.
Abstract
We develop a semi-Lagrangian algorithm for solving the three-dimensional advection problem. A numerical solution is determined on a uniform cubic grid as a piecewise trilinear function. The method is based on the integral balance equation between two neighboring time levels. The domain of integration at the previous time level is a curved cuboid. To compute an integral over this domain numerically, we approximate this cuboid by another one with the same 8 vertices. The latter cuboid is obtained by a trilinear (isoparametric) transformation of the unit cube. This leads to the integration over the unit cube with the help of the composite midpoint rule. Such a technique provides the validity of the local balance equation and does not involve computational and algorithmic complexity for solving the three-dimensional problem. The numerical experiments confirm the first-order convergence.
Year
DOI
Venue
2016
10.1007/978-3-319-57099-0_68
Lecture Notes in Computer Science
Keywords
Field
DocType
Semi-Lagrangian method,Advection equation,Isoparametric transformation,Local conservation
Convergence (routing),Mathematical analysis,Midpoint method,Balance equation,Integral element,Cuboid,Unit cube,Numerical analysis,Piecewise,Mathematics
Conference
Volume
ISSN
Citations 
10187
0302-9743
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Vladimir Shaydurov102.03
A. V. Vyatkin201.35
Elena Kuchunova300.34