A family of eulerian-lagrangian localized adjoint methods for multi-dimensional advection-reaction equations

Hong Wang, Richard E. Ewing, Guan Qin, Stephen L. Lyons, Mohamed Al-Lawatia, Shushuang Man

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

We develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for first-order advection-reaction equations on general multi-dimensional domains. Different tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes, which are fully mass conservative, naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary conditions. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices, which can be efficiently solved by the conjugate gradient method in an optimal order number of iterations without any preconditioning needed. Numerical results are presented to compare the performance of the ELLAM schemes with many well studied and widely used methods, including the upwind finite difference method, the Galerkin and the Petrov-Galerkin finite element methods with backward-Euler or Crank-Nicolson temporal discretization, the streamline diffusion finite element methods, the monotonic upstream-centered scheme for conservation laws (MUSCL), and the Minmod scheme.

Original languageEnglish
Pages (from-to)120-163
Number of pages44
JournalJournal of Computational Physics
Volume152
Issue number1
DOIs
Publication statusPublished - Jun 10 1999

Fingerprint

Advection
advection
finite element method
Boundary conditions
boundary conditions
Finite element method
conjugate gradient method
preconditioning
Conjugate gradient method
eccentrics
conservation laws
Finite difference method
boundary value problems
upstream
Boundary value problems
iteration
Conservation
formulations
coefficients

Keywords

  • Advection-reaction equations
  • Characteristic methods
  • Comparison of numerical methods
  • Eulerian-Lagrangian methods
  • Linear hyperbolic problems
  • Numerical solutions of advection-reaction equations

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

A family of eulerian-lagrangian localized adjoint methods for multi-dimensional advection-reaction equations. / Wang, Hong; Ewing, Richard E.; Qin, Guan; Lyons, Stephen L.; Al-Lawatia, Mohamed; Man, Shushuang.

In: Journal of Computational Physics, Vol. 152, No. 1, 10.06.1999, p. 120-163.

Research output: Contribution to journalArticle

Wang, Hong ; Ewing, Richard E. ; Qin, Guan ; Lyons, Stephen L. ; Al-Lawatia, Mohamed ; Man, Shushuang. / A family of eulerian-lagrangian localized adjoint methods for multi-dimensional advection-reaction equations. In: Journal of Computational Physics. 1999 ; Vol. 152, No. 1. pp. 120-163.
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