A higher-order eulerian-lagrangian localized adjoint method for two-dimensional unsteady advection-diffusion problems

Research output: Contribution to journalArticle

Abstract

We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.

Original languageEnglish
Pages (from-to)324-336
Number of pages13
JournalJournal of Computational Mathematics
Volume30
Issue number3
DOIs
Publication statusPublished - May 2012

Fingerprint

Adjoint Method
Advection-diffusion
Diffusion Problem
Advection
Boundary conditions
Higher Order
Characteristics Method
General Boundary Conditions
Advection-diffusion Equation
Conserve
Order of Convergence
Test function
Transport Equation
Governing equation
Experiments
Numerical Experiment
Numerical Solution
Simulation
Framework

Keywords

  • Advection-diffusion equations
  • Biquadratic interpolation
  • Characteristic methods
  • Eulerian-Lagrangian methods

ASJC Scopus subject areas

  • Computational Mathematics

Cite this

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abstract = "We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.",
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AB - We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it 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 establish its order of convergence numerically.

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