Solution of advection diffusion equations in two space dimensions by a rational Eulerian Lagrangian localized adjoint method over hexagonal grids

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Abstract

We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.

Original languageEnglish
Pages (from-to)43-55
Number of pages13
JournalInternational Journal of Numerical Analysis and Modeling
Volume9
Issue number1
Publication statusPublished - 2012

Fingerprint

Adjoint Method
Advection-diffusion Equation
Advection
Hexagon
Grid
Characteristics Method
Rational function
Basis Functions
Experiments
Numerical Experiment
Numerical Solution
Simulation
Framework

Keywords

  • Advection-diffusion equations
  • Characteristic methods
  • Eulerianlagrangian methods
  • Rational basis functions

ASJC Scopus subject areas

  • Numerical Analysis

Cite this

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abstract = "We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.",
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AB - We present a characteristic method for the solution of the transient advection diffusion equations in two space-dimensions. This method uses Wachspress-type rational basis functions over hexagonal grids within the framework of the Eulerian Lagrangian localized adjoint methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes and generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and to investigate its convergence numerically.

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KW - Characteristic methods

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KW - Rational basis functions

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