Solution of convection—diffusion equation by the method of characteristics
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Numerical simulation of free surface incompressible liquid flows surrounded by compressible gas
Journal of Computational Physics
Journal of Computational Physics
Computers & Mathematics with Applications
ELLAM for resolving the kinematics of two-dimensional resistive magnetohydrodynamic flows
Journal of Computational Physics
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
A characteristics-mixed covolume method for a convection-dominated transport problem
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-dimensional advection-diffusion equations with all combinations of inflow and outflow Dirichlet, Neumann, and flux boundary conditions. The ELLAM formalism provides a systematic framework for implementation of general boundary conditions, leading to mass-conservative numerical schemes. The computational advantages of the ELLAM approximation have been demonstrated for a number of one-dimensional transport systems; practical implementations of ELLAM schemes in multiple spatial dimensions that require careful algorithm development are discussed in detail in this paper. Extensive numerical results are presented to compare the ELLAM scheme with many widely used numerical methods and to demonstrate the strength of the ELLAM scheme.